Question

a building in a downtown business area casts a shadow that measures 88 meters along the ground. the straight - line distance from the top of the building to the end of the shadow it creates is at a 32° angle with the ground. what is the approximate height of the building? round your answer to the nearest meter. the building is meters high.

Explanation:

Step1: Set up a right - triangle model

We have a right - triangle where the length of the shadow is the adjacent side to the angle of elevation and the height of the building is the opposite side. Let the height of the building be $h$. The length of the shadow $x = 88$ meters and the angle of elevation $\theta=32^{\circ}$. We use the tangent function, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$.

Step2: Apply the tangent formula

$\tan\theta=\tan(32^{\circ})=\frac{h}{88}$.
We know that $\tan(32^{\circ})\approx0.6249$. So, $h = 88\times\tan(32^{\circ})$.

Step3: Calculate the height

$h=88\times0.6249 = 54.9912\approx55$ meters.

Answer:

55