Question

1. given the diagram below. what is the least angle of elevation the plane can take off in order to clear the building. 78.46° 11.54° 78.69° 11.31°

Explanation:

Step1: Use the tangent function

In a right - triangle, \(\tan x=\frac{\text{opposite}}{\text{adjacent}}\). Here, the opposite side to the angle \(x\) is \(200\) ft and the adjacent side is \(1000\) ft. So, \(\tan x=\frac{200}{1000}\).

Step2: Simplify the fraction

\(\frac{200}{1000} = 0.2\). So, \(\tan x=0.2\).

Step3: Find the angle \(x\)

To find \(x\), use the inverse tangent function \(x = \tan^{-1}(0.2)\). Using a calculator, \(x\approx11.31^{\circ}\).

Answer:

\(11.31^{\circ}\)