Question

A Ladder that is 32 ft long leans against a building. The angle of elevation of the ladder is 70 degrees. To the nearest tenth of a foot how high off the ground is the top of the ladder?

A. 20.3 ft

B. 10.9 ft

C. 26.2 ft

D. 39.1 ft

Answer 1

30.1 ft.

Explanation:

Please find the attachment.

Let the top of the ladder be 'h' feet high off the ground.

We have been given that a 32 ft long ladder leans against a building. The angle of elevation of the ladder is 70 degrees.

Upon looking at our attachment we can see that the 32 ft long side is hypotenuse and side with length h feet is opposite side of the right triangle formed by ladder and building with respect to ground.

Since sine relates the opposite side of right triangle with hypotenuse, so we can set an equation as:

`\text{sin}=\frac{\text{Opposite}}{\text{Hypotenuse}}`

Upon substituting our given values we will get,

`\text{sin}(70^(\circ))=(h)/(32)`

`0.939692620786=(h)/(32)`

`0.939692620786*32=(h)/(32)*32`

`30.070163865152=h`

`h\approx 30.1`

Therefore, the top of the ladder is 30.1 feet high off the ground.

Answer 2

see the picture attached to better understand the problem

we know that
in the right triangle ABC
sin 70°=opposite side angle 70°/hypotenuse


in this problem
opposite side angle 70°=AB
hypotenuse=AC----> 32 ft
sin 70°=AB/32------> AB=32*sin 70°-----> AB=30.07 ----> AB=30.1 ft