A HOT AIR BALLOON IS 70 m ABOVE THE SEA. TWO BUOYS A AND B ARE DUE EAST OF THE BALLOON. THE ANGLE OF DEPRESSION FROM THE BALLOON TO BUOY A IS 60°. THE ANGLE OF DEPRESSION FROM THE BALLOON TO THE BUOY B IS 40°. CALCULATE DISTANCE AB.

Question

Henry · Accepted Answer

1.

We draw 2 rt triangles with a common vertical side:

1. Draw hor. line OB.
2. Locate point "A" to the left of "B" to form AB.
3. Draw a ver. line at O and label it 70 m.

4. Draw the hyp. of each triangle
with one going to A and B.

Tan60 = 70/OA, OA = 70/Tan60.

Tan40 = 70/OB, OB = 70/Tan40.

AB = OB - OA.