Question

A satellite orbiting the earth passes directly overhead at observation stations in Phoenix and Los Angles, 340 miles apart.
At an instant when the satellite is between these two stations, its angle of elevation is simultaneously observed to be 60° at Phoenix and 75° at Los Angeles.

How far is the satellite from Los Angeles?

Answer 1

Answer:

Step-by-step explanation:

1. The above question forms a triangle ∠XYZ;

where ∠X = 60°

∠Y = 75° and

∠Z = 180° - (60° + 75°) = 45°

And side XZ = x (the distance between the satellite and Phoenix)

side YZ = y (the distance between the satellite and Los Angeles) and

side XZ = 340 mi (the distance between Phoenix and Los Angeles)

Using the formula;

$\frac{x}{sinX} = \frac{y}{sinY} = \frac{z}{sinZ}$

$\frac{x}{sin75} = \frac{y}{sin60} = \frac{340}{sin45}$

$\frac{y}{sin60} = \frac{340}{sin45}$

$y =\frac{340 * sin60}{sin45}$

$y = \frac{340 * 0.8660}{0.7071}$

∴ $y = 414.4050mi (4d.p)$