From the top of a 15 m high building, the angle of depression of a car on the road is 30°. Find the distance of the car from the foot of the building. (Use √3 = 1.732)

1. 1 · Write what is given and what is to be found Given: building AB = 15 m, angle of depression of car C from A = 30°. To find: BC.
2. 2 · Draw the figure Vertical AB with a right angle at B; ground BC; dotted horizontal through A; mark 30° below it; mark ∠ACB = 30°.
3. 3 · Write the formula or theorem Angle of elevation of A from C = angle of depression = 30° (alternate angles). tan 30° = AB/BC.
4. 4 · Substitute 1/√3 = 15/BC, so BC = 15√3 m.
5. 5 · Use the value of √3 BC = 15 × 1.732 = 25.98 m.
6. 6 · Check and box the answer The car is about 25.98 m (nearly 26 m) from the building. An angle below 45° should give a distance longer than the height, and it does.

Scoring tip: Write 'alternate angles' as the reason when you move the angle of depression into the triangle. Examiners look for it.