Question
Mathematics Question on Boat and Stream
From the top of a light-house 60 m high with its base at the sea-level, the angle of depression of a boat is 15∘. The distance of the boat from the foot of the light-house is
A
(3−13−1)×(60m)
B
(3−13+1)×(60m)
C
(3−13+1)×(30m)
D
(3+13−1)×(30m)
Answer
(3−13+1)×(60m)
Explanation
Solution
The correct option is (B):
Given AB = 60m ∠ACB=15∘ To find BC:
Using identity tan(A−B)=1−tanAtanBtanA−tanB
tan15∘=(tan60∘−tan45∘)
1−tan60∘tan45∘(tan60∘−tan45∘)
1+33−1……..(i)
In△ABC
tan(15∘)=BCAB
3+13−1=BC60
BC=3−13+160