Question

Two climbers are at points A and B on a vertical cliff face. To an observer C, 40 m from the foot of the cliff, on the level ground, A is at an elevation of 48° and B of 57°. What is the distance between the climbers?

Answer 1

Let P be the foot of the cliff on level ground.

Then, ∠ACP = 48° and ∠BCP = 57°

∴  `(BP)/(PC) = tan 57^circ`

`=>` BP = 40 × 1.539 = 61.57 m 

Also, `(AP)/(PC) = tan 48^circ`

`=>` AP = 40 × 1.110 = 44.4 m

Hence, distance between the climbers = AB = BP – AP = 17.17 m