Question

javi is standing at the end of a 100 - foot - long hallway. he looks up at the top of the wall at the other end of the hallway, and the angle of elevation is 18 degrees. a banner hangs on this wall, and its length is exactly one - third the height of the wall. how long is the banner? 10.8 feet 10.3 feet 32.5 feet 31.7 feet

Explanation:

Step1: Find the height of the wall

We use the tangent function. In a right - triangle (hallway length is adjacent side, wall height is opposite side), \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Given \(\theta = 18^{\circ}\) and adjacent \(= 100\) feet. So, \(\tan(18^{\circ})=\frac{h}{100}\), then \(h = 100\times\tan(18^{\circ})\).
Using a calculator, \(\tan(18^{\circ})\approx0.3249\), so \(h = 100\times0.3249 = 32.49\) feet.

Step2: Find the length of the banner

The banner length \(L=\frac{1}{3}h\). Substitute \(h = 32.49\) into the formula: \(L=\frac{1}{3}\times32.49=10.83\approx10.8\) feet.

Answer:

10.8 feet