Heights and Distances Practice Test 2

Let A be the position of a person on the bank of a river and OP the tree on the opposite bank and ∠OAP = 60°. When the person retires to the position B, s.t.
AB = 40 m then ∠ OBP = 30°
Let OA = x m and OP = h m
In Δ OAP, OP = OA tan 60° = x√3
and in Δ OBP, OP = OB tan 30° =

(x+40)

√3

∴

(x+40)

√3

=x√3⇒x=20m