Law of sines (Math Problem)

Question

The pathway satellite orbiting the earth causes it to pass directly over two tracking stations A and B which are 40 km apart when the satellite is on one side of the two stations the angle of elevation at A and B are measured to be 70 degrees and 36 degrees.

How far is the satellite from station A? Round to 3 decimals places

How high is the satellite above the ground? Round to 3 decimal places

Answer 1

Draw and label a diagram!

h represents the height of the satellite.

x represents the distance from A to the point under the satellite

h / x = tan 70°

h = x tan 70°

h / tan 70° = x

h / (x + AB) = tan 36°

h = (x + AB) tan 36°

h = x tan 36° + AB tan 36°

(h - AB tan36°) / tan 36° = x

Equate the left sides of the two equations, solve for h.

Use the value of h to determine the value of x.