Question

the angle of elevation of a ladder is 19° and the ladder is 12 feet from the wall. what is the height of the ladder in feet? enter your answer as a number, rounded to tenths, with the appropriate unit, like this: 42.5 ft.

Explanation:

Step1: Identify the trigonometric relation

We have a right - triangle where the distance from the wall to the base of the ladder is the adjacent side ($x = 12$ ft) to the angle of elevation ($\theta=19^{\circ}$) and the height of the ladder on the wall is the opposite side ($y$). We use the tangent function $\tan\theta=\frac{y}{x}$.

Step2: Solve for the height $y$

Since $\tan\theta=\frac{y}{x}$, then $y = x\tan\theta$. Substitute $x = 12$ and $\theta = 19^{\circ}$. So $y=12\times\tan(19^{\circ})$.
We know that $\tan(19^{\circ})\approx0.3443$. Then $y = 12\times0.3443=4.1316$.

Step3: Round the answer

Rounding $4.1316$ to the nearest tenth gives $4.1$ ft.

Answer:

$4.1$ ft