Question

Please solve (20 points)

Answer 1

104.65 m

Explanation:

The plane with the smaller angle of depression is closer to the raft.

Taking the tan values of both planes :

Plane 1 (57°)

• tan 57° = 3000 + x / h
• 1.54 = 3000 + x / h
• h = 3000 + x / 1.54 (Equation 1)

Plane 2 (48°)

• tan 48° = x / h
• 1.11 = x/h
• h = x/1.11 (Equation 2)

Equate Equations 1 and 2 :

• 3000 + x / 1.54 = x/1.11
• 1.11 (3000 + x) = 1.54x
• 3330 + 1.11x = 1.54x
• 0.43x = 3330
• x = 77.44 m

Taking the sin ratio to find distance :

• sin 48° = 77.44/distance
• 0.74 = 77.44/distance
• distance = 77.44/0.74
• distance = 104.65 m