Question

1. 0 / 1 points my notes details my notes previous answers ask your teacher practice another a 32 - ft ladder leans against a building so that the angle between the ground and the ladder is 67°. how high does the ladder reach up the side of the building? (round your answer to four decimal places.) enter a number. ft hypotenuse. note that the angle of elevation is the angle opposite the height of the building. which trigonometric function is the ratio of the opposite side to the adjacent side? resources ebook determine length of right triangle side learn by example

Explanation:

Step1: Identify the trigonometric relation

We know the length of the hypotenuse (ladder length $c = 32$ ft) and the angle of elevation $\theta=67^{\circ}$, and we want to find the height $h$ (opposite - side to the angle) of the building that the ladder reaches. The sine function is defined as $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$.

Step2: Substitute the values into the sine formula

We have $\sin\theta=\sin(67^{\circ})=\frac{h}{32}$.

Step3: Solve for $h$

$h = 32\times\sin(67^{\circ})$. Since $\sin(67^{\circ})\approx0.9205$, then $h = 32\times0.9205=29.456$ ft.

Answer:

$29.4560$ ft