Heights and Distances Practice Test 2

Question : 1 of 24

Marks: +1, -0

A person standing on the bank of a river observes that the angle subtended by a tree on the opposite bank is 60°, when he retires 40 metres from the bank he finds the angle to be 30°. Then the breadth of the river is:

40 m
60 m
20 m
30 m

Validate

Solution:

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 = 20 m

Go to Question:

Next Question