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 (square) meters high.

Explanation:

Step1: Define trigonometric relation

We use the tangent function, where $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$. Here, $\theta=32^\circ$, adjacent side (shadow length) $=88$ m, opposite side is building height $h$.

Step2: Rearrange to solve for $h$

$h = 88 \times \tan(32^\circ)$

Step3: Calculate the value

Using $\tan(32^\circ) \approx 0.6249$, we get $h \approx 88 \times 0.6249$
$h \approx 54.9912$

Step4: Round to nearest meter

Round $54.9912$ to the nearest whole number.

Answer:

55