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: Identify the trigonometric relation

We have a right - triangle where the length of the shadow is the adjacent side ($x = 88$ meters) to the given angle $\theta=32^{\circ}$, and the height of the building is the opposite side ($y$) to the angle. We use the tangent function $\tan\theta=\frac{y}{x}$.

Step2: Solve for the height of the building

We know that $\tan\theta=\frac{y}{x}$, so $y = x\tan\theta$. Substituting $x = 88$ meters and $\theta = 32^{\circ}$, and $\tan32^{\circ}\approx0.6249$. Then $y=88\times0.6249\approx55$ meters.

Answer:

55