Question

determining height from a shadow
a building in a downtown business area casts a shadow that measures 88 meters along the ground. the straight - 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 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 to the given angle and the height of the building is the opposite side. We use the tangent function, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$.
Let $\theta = 32^{\circ}$ and the adjacent side $x = 80$ meters, and the height of the building be $h$ (opposite side). So, $\tan\theta=\tan(32^{\circ})=\frac{h}{80}$.

Step2: Solve for the height $h$

We can re - arrange the formula to get $h = 80\times\tan(32^{\circ})$.
We know that $\tan(32^{\circ})\approx0.6249$. Then $h = 80\times0.6249 = 49.992\approx50$ meters.

Answer:

50