The angle of depression of a ground point 9√3 metres from a building, seen from the top of the building, is 30°. What is the height of the building in metres?

Correct answer: b 9

h = 9√3 × tan 30° = 9√3 × 1/√3 = 9 metres. The depression and the angle at the ground are alternate angles, so that angle is 30° too.

Why the other options are wrong

• a 3√3: 3√3 comes from dividing 9√3 by 3; the rule is h = d × tan 30°, not a division by 3.
• c 9√3: 9√3 is the ground distance d itself; the height is d × tan 30° = 9.
• d 36: 36 is no step result; 9√3 × tan 30° = 9√3 × 1/√3 = 9.