Question

How long must a ladder be to reach the top of 20” wall if the ladder and the wall form a 32 angle at the top

Answer 1

23.97 ft

Explanation:

In this question apply the expression for determining cosine of an angle.

Cosine of an angle x°=length of the adjacent side÷hypotenuse

`Cos\alpha =(A)/(H)`

where α is the angle in degrees, A is the adjacent side length, and H is the hypotenuse

Given α=32° and A=20ft H=?

Applying the expression

`Cos\alpha =(A)/(H) \\\\Cos32=(20)/(H) \\\\0.8342=(20)/(H)\\ \\H=(20)/(0.8342) =23.97`

In this case, the length of the ladder represents the hypotenuse side of the triangle which will be 23.97 ft

Answer 2

Answer: 23.58

Explanation:

`cos\theta=(adjacent)/(hypotenuse)\\\\\\cos(32^o)=(20)/(x)\\\\\\x=(20)/(cos(32^o))\\\\\\x=23.58`