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UkoKoshka [18]
3 years ago
12

A 30 ft ladder leans against the side of a house. If the base of the ladder sits 10 ft away from the base of the house, what is

the ladder's angle of elevation?
Mathematics
1 answer:
musickatia [10]3 years ago
3 0

Answer:

70.5°

Step-by-step explanation:

To solve for the ladder's angle of elevation, we solve using the Trigonometric function of Cosine

= cos θ = Adjacent/Hypotenuse

Where

Adjacent = Distance of the base from the house = 10ft

Hypotenuse = Length of the ladder = 30 ft

cos θ = 10/30

cos θ = 1/3

θ = arc cos 1/3

θ = 70.528779366

Approximately = 70.5°

Therefore, the ladder's angle of elevation is 70.5°

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Use appropriate identities to rewrite the wave equation shown below in the form ℎ(x) = a cos (x − c).
yarga [219]

Answer:

h(x) = 10 cos(x-36.870)

Step-by-step explanation:

Note: For this problem we use the calculator on degrees

For this case we need to remember this identity :

Cos (a-b) = cos a cos b + sin a sin b

For this case if we apply for our desired formula we got this:

a cos (x-c) = a [cos (c) cos (x) + sin (c) sin (x)]

And we want this equal to h(x) = 6 sin (x) + 8 cos (x) so we can set up the following equality:

6 sin (x) + 8 cos (x)= a cos (c) [cos (x)] + a sin (c) [sin(x)]   (1)

If we apply direct comparison between the factors on equation (1) we see this:

a cos(c) = 8    (2)

a sin (c) = 6    (3)

If we solve a from equation (2) we got:

a = \frac{8}{cos (c)}   (4)

If we replace equation (4) into equation (3) we got:

\frac{8}{sin(c)} cos (c) = 8 tan (c) = 6

tan(c) = \frac{6}{8}=\frac{3}{4}

If we apply inverse tangent on both sides we got:

c = tan^{-1} (3/4) = 36.870

So then the value of c= 36.870 degrees. And since w ehave the value of c we can find the value for a and we got:

[tex] a = \frac{8}{cos (36.870)}=10

And then our expression in the form h(x) = a cos (x-c) is:

h(x) = 10 cos(x-36.870)

And we can check that:

h(x)= 10 cos (36.870) [cos (x)] + 10 sin (36.870) [sin(x)]= 8 cos (x) + 6 sin (x)

8 0
3 years ago
-8x + 4y =24<br> -7x + 7y = 28
Afina-wow [57]
<h2>I hope it will help you!!!!!</h2>

6 0
3 years ago
How tall is the tree?<br> 5ft<br> 35°<br> -20ft-<br> [? ]ft
Strike441 [17]

Answer:

19

Step-by-step explanation:

tan35=x/20

20tan35=x

x=14.0041507641942

x+5=19.0041507641942

Nearest foot is 19

5 0
2 years ago
M m =<br> 5m+100°<br> 2m+10°
Alex_Xolod [135]

Answer:

m= 20 for one becouse 5×20 is 100

m= 5 because 5×2 is 10

or do 5÷100 that is 20

and 2÷10 that is 5

4 0
3 years ago
A particular shade of paint is made by mixing 5 parts red paint with 7 parts blue paint. To make this shade, Shannon mixed 12 qu
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Shannon did not mix the correct shade. Cause the correct ratio of blue and red is 7:5. While Shannon mix 12:8=3:2 which is not equal to 7:5.
3 0
3 years ago
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