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 \boxed{} meters high.

Explanation:

Step1: Identify trigonometric ratio

We use tangent: $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$, where $\theta=32^\circ$, adjacent = 88 m, opposite = height $h$.

Step2: Rearrange to solve for $h$

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

Step3: Calculate the value

$\tan(32^\circ) \approx 0.6249$, so $h \approx 88 \times 0.6249$
$h \approx 54.9912$

Step4: Round to nearest meter

Round 54.9912 to 55.

Answer:

55