Question

a 35 - ft ladder leans against a building so that the angle between the ground and the ladder is 66°. how high does the ladder reach up the side of the building? (round your answer to four decimal places.)

Explanation:

Step1: Identify the trigonometric relationship

We have a right - triangle where the length of the ladder is the hypotenuse ($c = 35$ ft) and we want to find the height ($a$) the ladder reaches up the building. The angle between the ground and the ladder is $\theta=66^{\circ}$. We use the sine function since $\sin\theta=\frac{a}{c}$.

Step2: Solve for the height

We can rewrite the sine formula as $a = c\times\sin\theta$. Substitute $c = 35$ and $\theta = 66^{\circ}$ (in radians, $\theta=66\times\frac{\pi}{180}$). But using a calculator in degree - mode, $a = 35\times\sin(66^{\circ})$.
$a=35\times0.913545 = 31.974175\approx31.9742$

Answer:

$31.9742$