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 relationship

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 ($y$). We use the tangent function $\tan\theta=\frac{y}{x}$.

Step2: Rearrange the formula to solve for $y$

$y = x\tan\theta$. Substitute $x = 88$ and $\theta = 32^{\circ}$. Since $\tan32^{\circ}\approx0.6249$, then $y=88\times0.6249$.

Step3: Calculate the value of $y$

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

Answer:

55