From the top of a forest watchtower 25 m high, the angle of depression of a deer standing on one side is 45°, and the angle of depression of a jeep standing on the exactly opposite side, in the same straight line, is 30°. Find the exact distance (in m) between the deer and the jeep.

Question

Accepted Answer

25(√3 + 1). Deer: tan 45 = 25/d1 => d1 = 25 m. Jeep: tan 30 = 25/d2 => d2 = 25 √3 m. They are on OPPOSITE sides of the tower, so the distance between them = 25 + 25 √3 = 25(√3 + 1) m (about 68.3 m). Subtracting would be correct only if both were on the same side.

From the top of a forest watchtower 25 m high, the angle of depression of a deer standing on one side is 45°, and the angle of depression of a jeep standing on the exactly opposite side, in the same straight line, is 30°.
Find the exact distance (in m) between the deer and the jeep.

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 10 Heights and Distances practice

From the top of a forest watchtower 25 m high, the angle of depression of a deer standing on one side is 45°, and the angle of depression of a jeep standing on the exactly opposite side, in the same straight line, is 30°.Find the exact distance (in m) between the deer and the jeep.

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 10 Heights and Distances practice

From the top of a forest watchtower 25 m high, the angle of depression of a deer standing on one side is 45°, and the angle of depression of a jeep standing on the exactly opposite side, in the same straight line, is 30°.
Find the exact distance (in m) between the deer and the jeep.