A man finds that the angle of elevationof a building is 22º. After walking 20 m towards the building, he finds that the angle of elevation is 33º. Find the height of the
building?
Answers
Answer:
The height of the building is 21.38 m
Step-by-step explanation:
Trigonometric Ratios
The ratios of the sides of a right triangle are called trigonometric ratios.
The image attached shows the measures and angles provided in the problem. The first angle of elevation is y=22°, the man walks B=20 m and finds the new angle of elevation is x=33°.
It's required to find the height of the building H.
The tangent ratio relates the opposite side with the adjacent side of a given angle. Applying it to the larger triangle:
[tex]\displaystyle \tan y=\frac{\text{opposite leg}}{\text{adjacent leg}}[/tex]
[tex]\displaystyle \tan 22^\circ=\frac{H}{D+B}[/tex]
Multiplying by D+B:
[tex]\tan 22^\circ(D+B)=H[/tex]
Dividing by tan 22°
[tex]\displaystyle D+B=\frac{H}{\tan 22^\circ}[/tex]
Subtracting B:
[tex]\displaystyle D=\frac{H}{\tan 22^\circ}-B\qquad\qquad[1][/tex]
Applying to the smaller triangle:
[tex]\displaystyle \tan 33^\circ=\frac{H}{D}[/tex]
Multiplying by D:
[tex]\tan 33^\circ D=H[/tex]
Substituting from [1]:
[tex]\displaystyle \tan 33^\circ \left(\frac{H}{\tan 22^\circ}-B\right)=H[/tex]
Substituting values:
[tex]\displaystyle 0.6494 \left(\frac{H}{0.4040}-20\right)=H[/tex]
Operating:
[tex]1.6074H-12.988=H[/tex]
[tex]1.6074H-H=12.988[/tex]
[tex]0.6074H=12.988[/tex]
[tex]H = 12.988/0.6074[/tex]
H = 21.38 m
The height of the building is 21.38 m
Related Questions
What is the slope of that line?
Answers
Answer:
the slope is 1
Step-by-step explanation:
left to right is positive and from the first dot it's one up and one over or 1/1 and that continues all the way up
Hope this helps have a good day!!! :))
Which set of ordered pairs (x,y)(x,y) could represent a linear function? \mathbf{A}= A= \,\,\left\{(2, 9),\,\,(4, 5),\,\,(6, 1),\,\,(7, -1)\right\} {(2,9),(4,5),(6,1),(7,−1)} \mathbf{B}= B= \,\,\left\{(-1, -8),\,\,(0, -3),\,\,(1, 3),\,\,(2, 8)\right\} {(−1,−8),(0,−3),(1,3),(2,8)} \mathbf{C}= C= \,\,\left\{(-9, 5),\,\,(-3, 3),\,\,(3, 0),\,\,(9, -2)\right\} {(−9,5),(−3,3),(3,0),(9,−2)} \mathbf{D}= D= \,\,\left\{(1, -8),\,\,(2, -6),\,\,(3, -3),\,\,(4, 0)\right\} {(1,−8),(2,−6),(3,−3),(4,0)}
Answers
Question:
Which set of ordered pairs (x,y) could represent a linear function?
[tex]\mathbf{A}= \,\,\left\{(2, 9),\,\,(4, 5),\,\,(6, 1),\,\,(7, -1)\right\}[/tex]
[tex]\mathbf{B}= \,\,\left\{(-1, -8),\,\,(0, -3),\,\,(1, 3),\,\,(2, 8)\right\}[/tex]
[tex]\mathbf{C}= \,\,\left\{(-9, 5),\,\,(-3, 3),\,\,(3, 0),\,\,(9, -2)\right\}[/tex]
[tex]\mathbf{D}= \,\,\left\{(1, -8),\,\,(2, -6),\,\,(3, -3),\,\,(4, 0)\right\}[/tex]
Answer:
[tex]\mathbf{A}= \,\,\left\{(2, 9),\,\,(4, 5),\,\,(6, 1),\,\,(7, -1)\right\}[/tex]
Step-by-step explanation:
Given
Ordered pairs A - D
Required
Which represents a linear function?
To do this, we simply calculate the slope (m) of each ordered pairs.
[tex]m = \frac{y_2 - y_1}{x_2-x_1}[/tex]
Considering A:
[tex]\mathbf{A}= \,\,\left\{(2, 9),\,\,(4, 5),\,\,(6, 1),\,\,(7, -1)\right\}[/tex]
Consider the following pairs
[tex](x_1,y_1) = (2,9)[/tex] and [tex](x_2,y_2) = (4,5)[/tex]
[tex]m = \frac{5 - 9}{4 -2} = \frac{-4}{2} = -2[/tex]
Consider the another pairs
[tex](x_1,y_1) = (2,9)[/tex] and [tex](x_2,y_2) = (6,1)[/tex]
[tex]m = \frac{1 - 9}{6 -2} = \frac{-8}{4} = -2[/tex]
Consider the another pairs
[tex](x_1,y_1) = (2,9)[/tex] and [tex](x_2,y_2) = (7,-1)[/tex]
[tex]m = \frac{-1 - 9}{7 -2} = \frac{-10}{5} = -2[/tex]
The slope is uniform all through.
i.e.
[tex]m = -2[/tex]
Hence, this can be a linear function
Considering B:
[tex]\mathbf{B}= \,\,\left\{(-1, -8),\,\,(0, -3),\,\,(1, 3),\,\,(2, 8)\right\}[/tex]
Consider the following pairs
[tex](x_1,y_1) = (-1,-8)[/tex] and [tex](x_2,y_2) = (0,-3)[/tex]
[tex]m = \frac{-3 - (-8)}{0 - (-1)} = \frac{-3 +8}{0 +1} = \frac{5}{1} = 5[/tex]
Consider the another pairs
[tex](x_1,y_1) = (-1,-8)[/tex] and [tex](x_2,y_2) = (1,3)[/tex]
[tex]m = \frac{3 - (-8)}{1 - (-1)} = \frac{3 +8}{1 +1} = \frac{11}{2} = 5.5[/tex]
The calculated slopes are not equal.
i.e.
[tex]m = 5[/tex] and [tex]m = 5.5[/tex]
Hence, this can't be a linear function
Considering C:
[tex]\mathbf{C}= \,\,\left\{(-9, 5),\,\,(-3, 3),\,\,(3, 0),\,\,(9, -2)\right\}[/tex]
Consider the following pairs
[tex](x_1,y_1) = (-9,5)[/tex] and [tex](x_2,y_2) = (-3,3)[/tex]
[tex]m=\frac{3-5}{-3-(-9)} = \frac{3-5}{-3+9} = \frac{-2}{6} = -\frac{1}{3}[/tex]
Consider the another pairs
[tex](x_1,y_1) = (-9,5)[/tex] and [tex](x_2,y_2) = (3,0)[/tex]
[tex]m=\frac{0-5}{3-(-9)} = \frac{0-5}{3+9} = \frac{-5}{12} = -\frac{5}{12}[/tex]
The calculated slopes are not equal.
i.e.
[tex]m = -\frac{5}{12}[/tex] and [tex]m = -\frac{1}{3}[/tex]
Hence, this can't be a linear function
Considering D:
[tex]\mathbf{D}= \,\,\left\{(1, -8),\,\,(2, -6),\,\,(3, -3),\,\,(4, 0)\right\}[/tex]
Consider the following pairs
[tex](x_1,y_1) = (1,-8)[/tex] and [tex](x_2,y_2) = (2,-6)[/tex]
[tex]m = \frac{-6 - (-8)}{2 - 1} = \frac{6 + 8}{1} = \frac{14}{1} = 14[/tex]
Consider the another pairs
[tex](x_1,y_1) = (1,-8)[/tex] and [tex](x_2,y_2) = (3,-3)[/tex]
[tex]m = \frac{3 - (-8)}{-3 - 1} = \frac{3 + 8}{-4} = \frac{11}{-4} = -\frac{11}{4}[/tex]
The calculated slopes are not equal.
i.e.
[tex]m = -\frac{11}{4}[/tex] and [tex]m = 14[/tex]
Hence, this can't be a linear function
From the calculations above:
Only (A) can be a linear function
Answer:
Step-by-step explanation:
independent practice: tangents of circles
Line AB and Line CD are tangents of circle O. Find each of the following.
(see picture)
Answers
Answer:
here is your answer
Step-by-step explanation:
i.think this is a wrong question
Elsie bought a video game for $85.00. If the store charges 170% of it's cost for the game, how much is the store's profit?
Answers
Answer:
The stores profit is $59.50
Step-by-step explanation:
Answer:
It is?
Step-by-step explanation:
Today the school's math club has $75 in its account. Yesterday the club members spent $27.75 on fees to enter a competition. The equation 75=a-27.7575=a−27.75 represents this situation. What does the variable : a represent in this situation?
Answers
Answer:
a represents the amount of money that the math club had yesterday in its account.
Step-by-step explanation:
the account currently has $75.Yesterday, they spent $27.75 in fee to enter a competition, so that means that before they paid the fees, the math club's account had $75 + $27.75 = $102.75
What is thirty divided by ten
Answers
Answer:
It is three.................
30 ÷ 3 = 3
Hope this helps :)
A cooling tower is 120 meters tall. The sides of the tower are in the shape of a hyperbola defined by the equation x^2/500 - y^2/900 = 1 with units in meters. The center of the tower is at the origin. How wide is the tower at the top?
50 m
92 m
100 m
184 m
Answers
Answer:
c (100)
Step-by-step explanation:
on edg 2021 ^u^
The width of the tower at the top will be 92 m. Then the correct option is B.
What is a hyperbola?The hyperbola is the locus of a point such that the difference of distance from point P to two non-movable points. These two points are called foci of hyperbola.
A cooling tower is 120 meters tall.
The sides of the tower are in the shape of a hyperbola defined by the equation x²/500 – y²/900 = 1 with units in meters.
The center of the tower is at the origin.
Then the width of the tower at the top will be
x²/500 – (120)²/900 = 1
x²/500 – 14400/900 = 1
x²/500 – 16 = 1
x²/500 = 1 + 16
x²/500 = 17
x² = 8500
x = 92.19 ≈ 92 m
Then the correct option is B.
More about the hyperbola link is given below.
https://brainly.com/question/12919612
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PLEASE HELP!!!!!!!!!!
Answers
Answer:
a
Step-by-step explanation:
because add all then divied all the mutiply the too numbers
write the equation of the line that passes through the point (2,-3) and is perpendicular to the line y=-2x+3. And how do you find it?
Answers
Answer:
y=2x-7
Step-by-step explanation:
The easiest way to answer this would be by using the slope-intercept form equation, y=mx+b. In this case, we can use our given in information to plug in values and find the equation.
Firstly, let's assess what know and what we don't:
Given the point (2,-3), we know that x=2 and y=-3. Now the slope for a perpendicular line can be found using a negative reciprocal, since the product of the slopes of both lines should equal -1. Therefore the slope must be 2.
All that's left is b, the y-intercept. To solve for this, we simply plug in what we have.
y=mx+b
-3=2(2)+b
-3=4+b
-3-4=b
-7=b
Now that we have b, we can write the equation:
y=2x-7
Pls help due in 7 mins,ill give brainliest and 5 stars and thank you
Answers
Answer:
Step-by-step explanation:
a) 14x
b)-40c
c)8n
d)28x
e)8n
f)-15/2y= - 7 1/2 y
Please help me with number 15. If you could provide work, that would be great.
Answers
x[tex]x^{2} -10x+9--->use AC method---->(x-9)(x-1)[/tex] i think
please help asap !!!
Answers
Answer:
The solution to the system of equation is (1,-4)
Step-by-step explanation:
Here, we want to find the solution to the system of equations
Since we have y in both places, we can equate the two
That would be;
-x-3 = -7x + 3
-x + 7x = 3 + 3
6x = 6
x = 6/6
x = 1
y = -x - 3
y = -1 -3
y = -4
So the solution to the system of equations is (1,-4)
74% of the animals at an animal shelter are dogs. About what fraction of the animals at the shelter are dogs? and also what is the equivalent fraction to 74/100
Answers
Answer:
Thus, 37/50 is the equivalent fraction to 74/100.
Therefore, 37/50 of the animals in the shelter are dogs.
Step-by-step explanation:
Given
Given that 74% of the animals at an animal shelter are dogs.
To determine:
About what fraction of the animals at the shelter are dogs?
Using the equation to find a fraction equivalent to 74%
[tex]\:74\%=\:\frac{74}{100}[/tex]
Divide numerator and denominator by 2
[tex]=\frac{\frac{74}{2}}{\frac{100}{2}}\:\:[/tex]
Cancel the common factor 2.
[tex]=\frac{37}{50}[/tex]
Thus, 37/50 is the equivalent fraction to 74/100.
Therefore, 37/50 of the animals in the shelter are dogs.
Why is it not possible to make a right triangle using lengths 20 feet, 40 feet, and 50 feet?
A. 20+ 40 is greater than 50
B. 50- 40 does not equal 20
C. 20 squared + 40 squared does not equal 50 squared
D. (20+40) squared is greater than 50 squared
Answers
Answer:
its actually joe to the we of the ner
5,0,-5,-10
Next three terms of the arithmetic sequence
Answers
The diagram shows ASTU. Which term describes point V?
A. Circumcenter
B. Orthocenter
C. Incenter
D. Centroid
Answers
Answer:
orthocenter
Step-by-step explanation:
I just did it
The term which describes the point V is Orthocenter, the correct option is B.
What is centroid of a triangle and its coordinates?
The point of intersection of a triangle's medians is its centroid (the lines joining each vertex with the midpoint of the opposite side).
If the triangle has its vertices as [tex](x_1, y_1), (x_2, y_2) , \: (x_3, y_3)[/tex], then the coordinates of the centroid of that triangle is given by:
[tex](x,y) = \left( \dfrac{x_1 + x_2 + x_3}{3} + \dfrac{y_1 + y_2 + y_3}{3} \right)[/tex]
We are given that;
The figure
Now,
We know that in a triangle, whenever a line that passes through a vertex of the triangle such that is perpendicular to the opposite side is called an altitude of the triangle;
So, the point where all the three altitudes of the triangle meets is called its orthocenter .
From the given figure , we can conclude that the point V is the intersecting points of all the altitudes of the triangle STU.
Therefore, by centroid concept the answer will be Orthocenter.
Learn more about centroid here:
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Please help! I dont understand how to solve this problem! please show work/ explain how to do this. :D
Answers
Answer:
1Step-by-step explanation:
[tex]\frac{\sqrt[3]{7}\sqrt{7} }{\sqrt[6]{7^{5} } } \\\\=\frac{7^{\frac{1}{3}+\frac{1}{2}}}{\sqrt[6]{7^5}}\\\\=\frac{7^{\frac{5}{6}}}{\sqrt[6]{7^5}}\\\\=\frac{7^{\frac{5}{6}}}{\left(7^5\right)^{\frac{1}{6}}}\\\\=\sqrt[6]{\frac{7^5}{7^5}}\\\\=\sqrt[6]{1}\\\\=1[/tex]
Solve: (4.5 x 10^4)/ (300)
Please and Thank you.
Answers
(2): "4.5" was replaced by "(45/10)"
1.1 10 = 2•5
(10)4 = (2•5)4 = 24 • 54
45
(—— • (x(2^4•5^4))) ÷ 300
10
9
Simplify —
2
9
— • x10000) ÷ 300
2
9x10000
——————— ÷ 300
2
9x10000
Divide ——————— by 300
2
Final result :
3x10000
———————
200
Answer:
150 plz brainliest
Step-by-step explanation:
10^4 = 10000
10000 (4.5) = 45,000
45,000/300 = 150
I need someone to answer 30-35
Answers
5. MRS. SANTOS RECEIVED 7% COMMISSION AFTER SELLING A
PIECE OF PROPERTY WORTH PHP 850 000. HOW MUCH WAS
HER COMMISSION? helppppp me plssssssssss☹☹☹
Answers
Answer:
Mrs. Santos's commission was 59,500.
Step-by-step explanation:
850,000 * 7% = 59,500
Mr. Green paid $7.50 for a set of dry erase markers. He used a $2.00 coupon for his purchase. Write AND solve an equation that represents the difference between d, the original price of the markers and the coupon. Solve for d.
Answers
Answer:
[tex]d - 2 = 7.50[/tex]
$9.50
Step-by-step explanation:
Given that:
Money paid by Mr. Green for a set of dry erase markers = $7.50
Coupon used for the purchase = $2.00
To find:
The equation and solution to represent the difference the original price [tex]d[/tex] of the markers and the coupon.
Solution:
Given that, the original price of the dry erase markers = $[tex]d[/tex]
Coupon amount = $2.00
Amount paid = $7.50
The equation can be made by subtracting the coupon amount from the original price and comparing it with the amount paid by Mr. Green for the purchase.
Original price = $([tex]d[/tex] - 2)
[tex]d - 2 = 7.50[/tex]
Solving the above equation by adding 2 on both the sides:
[tex]d -2+2= 7.50+2\\\Rightarrow d = \$9.50[/tex]
Solve for x: 3x + 4 = 9x + 3
Answers
Answer:
Step-by-step explanation:
3x+4=9x+3, we will add and subtract the variable and the numbers so we have, x in one side and the numbers on the other side
4-3=9x-3x
1=6x
x=1/6
Answer:
x = 1/6
Step-by-step explanation:
1. Add and subtract the variable and the numbers.
So far: 4 - 3 = 9x - 3x
4 - 3 = 9x - 3x
2. Simplify.
4 - 3 = 1.
9x - 3x = 6x.
To do addition with variables, delete the variables, which now is 9 - 3, easy, 6, add the x back (only to the answer), so 6x.
Since 1 is on 1 part of the equal side, because 4 - 3 = 1.
And is 1 = 6x.
1/6 then is your final answer.
24 in
45 in
What is the length of the hypotenuse?
Answers
Step-by-step explanation:
c²=24²+45²=2601
so c=51
If L II M, solve for x and y
I’ll give Brainliest to best answer
Answers
Answer:
x=17
y=9
Step-by-step explanation:
set 3x-4=5x-38
-2x=-34
x=17
plug x back into equa.= 47 degrees
180-90(right angle)-47=43
7y-20=43
7y=63
y=9
8x^2-5x-4
can anyone solve this its a question on my homework?
Answers
Answer:
x = 1.09 , − 0.46
Step-by-step explanation:
→ Factorise 8x² - 5x - 4
Not possible by factorisation
→ Substitute values into quadratic formula
x = 1.09 , − 0.46
THIS IS SIMPLE INTEREST
Interest = $10
Principal = $250
Interest rate = 4%
Time = ?
Answers
Step-by-step explanation:
mmi got the answer .as : 1
time=1
Kay works as a salesperson in a local department store. Kay earns a salary of $150.00 per
week plus a commission of 5% of the total sales.
Find Kay's total earning for a week when the store's total sales are $8.000.00.
A. $40,150.00
B. $4, 150.00
C. $550.00
D. $190.00
E. $407.50
Answers
Answer:
$550.00
Step-by-step explanation:
I just looked up what is 5℅ of 8,000.00 and added that to her weekly salary
Answer:
The answer would be 550$
Step-by-step explanation:
Danielle picks 744 apples at an apple orchard. She divides the apples equally into 40 baskets.
Part A
When dividing 744 ÷ 40, the first digit of the quotient will be in what place?
Hundreds
Tens
Ones
Thousands
Part B
How many apples will be in each basket? Enter your answer in the box.
apples=??
Part C
How many apples will be left? Enter your answer in the box.
apples=??
Answers
Answer:
Step-by-step explanation:
Part A
When dividing 744 ÷ 40, the first digit of the quotient will be in what place?
Hundreds ✔️
Tens ❌
Ones ❌
Thousands
Part B
How many apples will be in each basket? Enter your answer in the box.
Apple in each box = 186
Part C
How many apples will be left? Enter your answer in the box.
Apple will be left = 0
Please Tell If Wrong Because I used a piece of paper
There are 18 apples in each basket from the given situation.
Given that, Danielle picks 744 apples at an apple orchard. She divides the apples equally into 40 baskets.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Part A:
744 ÷ 40
40 | 744 | 18
40
_____
344
320
_____
24
The first digit of quotient 18 is in tens place.
Part B:
There are 18 apples in each basket.
Part C:
There are 24 apples will be left.
Therefore, there are 18 apples in each basket from the given situation.
To learn more about the unitary method visit:
brainly.com/question/22056199.
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The Green family is planning a one-week vacation in Florida and needs to rent a car while there.
Answers
Answer:
they need a stimlus check
Step-by-step explanation:
facts
Rick will participate in a walk–a–thon to raise money for charity. The amount he will raise based on the number of miles he walks is shown in the table, which represents a linear function.
Miles Walked Amount Raised ($)
2 220
5 460
8 700
11 940
Which of these statements are correct? Select all that apply.
For each mile that Rick walks, he will raise an additional $110.
For each mile that Rick walks, he will raise an additional $80.
If Rick walks 0 miles, he will raise $60.
If Rick walks 0 miles, he will raise $80.
If Rick walks 0 miles, he will raise $0.
For each mile that Rick walks, he will raise an additional $60.
Answers
Answer:
the first one is correct
Step-by-step explanation: