Question

a 20 - ft ladder is leaning against a building. if the base of the ladder is 7 ft from the base of the building, what is the angle of elevation of the ladder? (round your answer to one decimal place.)
how high does the ladder reach on the building? (round your answer to the nearest whole number.)

Explanation:

Step1: Find the angle of elevation

Let the angle of elevation be $\theta$. We know the adjacent side ($a = 7$ ft) to the angle $\theta$ and the hypotenuse ($c=20$ ft) of the right - triangle formed by the ladder, the building and the ground. We use the cosine function $\cos\theta=\frac{a}{c}$. So, $\cos\theta=\frac{7}{20}=0.35$. Then $\theta=\cos^{- 1}(0.35)\approx69.5^{\circ}$.

Step2: Find the height on the building

Let the height on the building be $h$. Using the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $a = 7$, $c = 20$ and $b$ is the height $h$. So $h=\sqrt{c^{2}-a^{2}}=\sqrt{20^{2}-7^{2}}=\sqrt{400 - 49}=\sqrt{351}\approx19$ ft.

Answer:

$69.5$
$19$