Question

the base of a ladder is 10 feet away from a vertical building. the ladder tops at the top of the building. the ladders angle of elevation from the bottom of the ladder to the top of the building is 70°. what is the height of the building? 27.47 ft. 13.94 ft. 41.76 ft. 53.30 ft. 32.14 ft.

Explanation:

Step1: Identify the trigonometric relationship

We have a right - triangle where the adjacent side to the angle of elevation is the distance from the base of the ladder to the building ($x = 10$ feet) and we want to find the opposite side (height of the building $h$). We use the tangent function since $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$.
$\tan\theta=\frac{h}{x}$

Step2: Substitute the given values

Given $\theta = 70^{\circ}$ and $x = 10$ feet. We know that $\tan70^{\circ}\approx2.7475$. Substituting into the formula $\tan\theta=\frac{h}{x}$, we get $h=x\tan\theta$.
$h = 10\times\tan70^{\circ}$

Step3: Calculate the height

$h=10\times2.7475 = 27.475\approx27.47$ feet.

Answer:

27.47 ft.