From the top of a hill 40√3 m high, the angle of depression of a bus stop on the road below is 30°. Find the distance of the bus stop from the foot of the hill.

1. 1 · Write what is given and what is to be found Given: height AB = 40√3 m, angle of depression 30°. To find: BC, the distance of the bus stop C from the foot B.
2. 2 · Draw the figure Vertical AB, ground BC, dotted horizontal line at A. Mark 30° between the dotted line and AC, then 30° at C. Mark the right angle at B.
3. 3 · Write the reason and the formula ∠ACB = 30° (alternate angles). tan θ = opposite/adjacent, and tan 30° = 1/√3.
4. 4 · Work it out
   • tan 30° = AB/BC
   • 1/√3 = 40√3/BC
   • BC = 40√3 × √3 = 40 × 3 = 120 m
5. 5 · Does it make sense? 120 m is about a two-minute walk, a sensible distance to a bus stop.
6. 6 · Check and box the answer The bus stop is 120 m from the foot of the hill.

Scoring tip: Keep √3 as √3 here. Since √3 × √3 = 3, the answer is exact and you do not need 1.732.