Question

from the top of a hill the angles of depression of two consecutive kilometre stones D and C due west are found to be 30°and 60°. Find the height of the hill.​

Answer 1

Answer:

180 m

Step-by-step explanation:

as we all know that each angle is 60

Answer 2

The height of hill=1.73 km

Step-by-step explanation:

Let h be the height of the hill

In triangle ABC

$\theta=60^{\circ}$

BC=x km

$\frac{Perpendicular\;side}{Base}=tan\theta$

Using the formula

$\frac{AB}{BC}=\frac{h}{x}=tan60^{\circ}$

$\frac{h}{x}=\sqrt 3$

Using $tan60^{\circ}=\sqrt 3$

$h=x\sqrt 3$....(1)

In triangle ABD

$\theta=30^{\circ}$

BD=x+x+1=2x+1 km

$\frac{h}{2x+1}=tan30^{\circ}=\frac{1}{\sqrt3 }$

Using $tan30^{\circ}=\frac{1}{\sqrt 3}$

$h=\frac{2x+1}{\sqrt 3 }$...(2)

From equation (1) and equation (2)

$x\sqrt3 =\frac{2x+1}{\sqrt 3}$

$3x=2x+1$

$3x-2x=1$

$x=1$

Substitute the values

$h=\sqrt 3=1.73 km$

Hence, the height of hill=1.73 km

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https://brainly.in/question/3029040:Answered by Nikitasingh