Question

The angle of depression of two boat observed from the top of a light house 250 m
high are 45° and 60° respectively. If the boats are on the opposite sides of the light
house, find the distance between the boat correct to nearest whole number.​

Answer 1

See the diagram i have given below. After that, look at the explanation.

We have to find the length of BC

∠BAD = 90 - 60 = 30°. So, ∠ABD = 60°

∠DAC = 90 - 45 = 45°. so, ∠ACD = 45°

From these, we get BD = 250/tan60 = 250/√3

DC = 250/tan45 = 250/1 = 250

So, the distance between the boats = BD+DC = (250/1.732)+250

144.3 + 250 = 394.3 = 394 m

Hope it helps. Thank you.