Question

1. michael, whose eyes are five feet off of the ground, is standing 30 feet away from the base of a build and looking up at a 50° angle of elevation to point on the edge of buildings roof. to the nearest foot, how tall is the building?

Explanation:

Step1: Set up the tangent function

Let \(h\) be the height from Michael's eyes - level to the roof. We know the adjacent side \(x = 30\) feet and the angle of elevation \(\theta=50^{\circ}\). Using the tangent function \(\tan\theta=\frac{h}{x}\), so \(h = x\tan\theta\).

Step2: Substitute the values

Substitute \(x = 30\) and \(\theta = 50^{\circ}\) into the formula. \(\tan(50^{\circ})\approx1.191753592\), then \(h=30\times\tan(50^{\circ})\approx30\times1.191753592 = 35.75260776\) feet.

Step3: Find the total height of the building

The total height of the building \(H=h + 5\). So \(H=35.75260776+5=40.75260776\approx41\) feet.

Answer:

The building is approximately \(41\) feet tall.