Question

the angle of depression of two ships from the top of light house are 45° and 30° towards east if the ships are 200m apart,find the height of the light house​

Answer 1

Answer:

let A and B be given ships OC

be the lighthouse

let hight of lighthouse = OC = H

in triangle OAC we have

tan 45 = OC/OA

so OA = H ....(i)

in triangle OBC

tan 30 = OC/OB

1/root 3=H / OA+200

H+200= H root 3 [using i]

H (root 3-1) = 200

H= 200 /root 3-1

by rationalisation and simplefication ,we

get H=100 (root 3+1)

Answer 2

Let A and B be given ships

OC be the Lighthouse

Let height of Lighthouse = OC = H

In triangle OAC, we have

Tan 45° = OC/OA

So OA = H..... (i)

In triangle, OBC

Tan 30° = OC/OB

1/√3 = H/OA + 200

OA + 200 = H√3

H + 200 = H√3 Using...... (i)

H(√3-1) = 200

H = 200/√3-1 X √3+1 /√3+1

H = 200 (√3+1) / 2

H = 100 ( √3+1)

H = 100 x 1.732 +1 (√3 = 1.732)

H = 273.2m