Question

Daryl measures the angle of elevation to be 62 degrees. Frances measures the angle of elevation to be 54 degrees. if the two enthusiasts are 28m apart, how far off the ground is the helicopter.

Answer 1

The helicopter is 27.38 m far off the ground

Explanation:

The drawing shown in the image below has all the measures and variables needed to solve the problem.

We need to find R, the height of the helicopter. We'll use the law of sines to find the length of side a.

`\displaystyle (28)/(\sin X)=(a)/(\sin 54^\circ)`

The angle X is the measure needed to complete 180°:

X = 180° - 54° - 62° = 64°

Solving for a:

`\displaystyle a=(28)/(\sin 64^\circ)\cdot \sin 54^\circ`

Calculating:

a = 31.11 m

Now using the sine ratio in the right triangle to the left side:

`\displaystyle \sin 62^\circ=(R)/(a)`

Solving for R:

`R=a\sin 62^\circ`

R=31.11*0.88

R = 27.38 m

The helicopter is 27.38 m far off the ground