From the top of a 40m fire tower, a fire ranger observes smoke in tower

Question

locations. One has a an angle of depression of 10o, and the
other has an angle of depression of 7o. Calculate the
distance between the smoke sightings when they are

a.) on opposite sides of the tower and in line with the tower.
b.) in perpendicular directions from the tower.

Answer 1

a) The distance to each fire is
X = 40/tan A where A is the depression angle. That would be 325.8 m for one fiore and 226.9 m for the other. If they are in opposite directions along the same line, add the two for their distance apart.
b) If the directions to the two fires are at right angles as seen from the tower, calculate the hypotenuse of the triangle (fire1, fire2 and tower) to get the distance between the fires.

Answer 2

thank you!