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

Answer:  23.58

Step-by-step explanation:

$cos\theta=\dfrac{adjacent}{hypotenuse}\\\\\\cos(32^o)=\dfrac{20}{x}\\\\\\x=\dfrac{20}{cos(32^o)}\\\\\\x=23.58$

Answer 2

Answer:

23.97 ft

Step-by-step explanation:

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

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

$Cos\alpha =\frac{A}{H}$

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

$Cos\alpha =\frac{A}{H} \\\\Cos32=\frac{20}{H} \\\\0.8342=\frac{20}{H}\\ \\H=\frac{20}{0.8342} =23.97$

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