Question

an object A on the ground is observed from two lighthouses p and q of equal height 10 m each if the angles of depression of the object from the lighthouses p and q are 45 degree and 30 degree respectively find the distance between the two lighthouses.

Answer 1

Let AB be the height of the light house & two ships be at C and D .

In ∆ABC,

tan 45° = AB/BC = P/B

1 = 100 /BC

[tan 45° = 1]

BC = 100 m

In ∆ABD

tan 30° = AB/BD

1/√3 = 100/(BC + CD)

1/√3 = 100/(100 + CD)

100 + CD = 100√3

CD = 100√3 - 100

CD = 100(√3 - 1)

CD = 100 (1.732 - 1)

[Given √3 = 1.732]

CD = 100 × 0.732

CD = 73.2 m

Hence, the distance between the two ships is 73.2 m