A girl on a ship standing on a wooden platform, which is 50 m above water level, observes the angle of elevation of the top of a hill as 30° and the angle of depression of the base of the hill as 60°. Calculate the distance of the hill from the platform and the height of the hill.​

Answers 2

Step-by-step explanation:

just draw diagram properly and then answer will come correct

answer img

Given

  • height of the wooden platform equal to 50 m
  • angle of elevation 30°
  • angle of depression is 60 degree

To find

  • the height of the hill
  • the distance between the hill and the point where the girls stands.

Solution

from the figure we can write, considering the triangle ABD

tan30 = AD/BD

or, tan30 = AD/d

or, d = AD/tan30

or, d= √3AD ....(1)

considering the triangle BDC

tan60 = DC/BD

or, tan60 = 50/d

or, d= 50/√3

or, d = 28.86m

distance of the girl from the hill is 28.86m

using equation 1

AD = 28.8/√3

Or, AD = 16.6m

therefore the height of the hill, AD + 50

Or, 16.6 + 50 = 66.6 m

answer img

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