Question

A man standing on the deck of ship, which is 10m above the water level, observes the angle of elevation  of  the  top  of  a  hill  as  60 and  the  angle  of  depression  of  the  base  of  the  hill  as  30 Calculate the distance of the hill from the ship and the height of the hill. ​

Answer 1

Answer:

Step-by-step explanation:

Let a man is standing on the Deck of a ship at point a such that AB = 10 m & let CE be the hill

Thus, AB = CD = 10 m

The top and bottom of a hill is E and C.

Given, the angle of depression of the base C of the hill observed from A is 30° and angle of elevation of the top of the hill observed from A is 60 °

Then ∠EAD= 60° &

∠CAE= ∠BCA= 30°. (Alternate ANGLES)

Let AD = BC = x m & DE= h m

In ∆ ADE

tan 60° = Perpendicular / base = DE/AD

√3= h/x [tan 60° = √3]

h = √3x……..(1)

In ∆ ABC

tan 30° = AB /BC

[ tan30° = 1/√3]

1/√3 = 10/x

x= 10√3 m.. …………..(2)

Substitute the value of x from equation (2) in equation (1), we have

h = √3x

h= √3× 10√3= 10 × 3= 30 m

h = 30 m

The height of the hill is CE= CD+ DE= 10 +30= 40 m

Hence, the height of the hill is 40 m & the Distance of the hill from the ship is 10√3 m.

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Hope this will help you...

Answer 2

Step-by-step explanation:

Find the distance of the hill from the ship and the height of the hill. Thus, AB = CD = 10 m The top and bottom of a hill is E and C. Hence, the height of the hill is 40 m & the distance of the hill from the ship is 10√3 m. Was this answer helpful?