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 (adjacent side) is \(x = 88\) meters and the angle with the ground is \(\theta=32^{\circ}\). The height of the building \(h\) is the opposite side with respect to the given angle. We use the tangent function: \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\).

Step2: Substitute the values into the formula

Since \(\tan\theta=\frac{h}{x}\), and \(x = 88\), \(\theta = 32^{\circ}\), we have \(h=x\tan\theta\). Substituting \(x = 88\) and \(\theta = 32^{\circ}\), we get \(h = 88\times\tan(32^{\circ})\).

Step3: Calculate the value

We know that \(\tan(32^{\circ})\approx0.6249\). Then \(h=88\times0.6249 = 55.0912\)

Answer:

\(55\)