Question

From a point on the ground the angle of elevation of a mountain is 45°.On walking 1km along the slope at 30°,the angle is found to be 60°.Find height of mountain.​

Answer 1

Step-by-step explanation:

$\huge\boxed{\fcolorbox{blue}{orange}{HELLO\:MATE}}$

Refer to attachment for figure:

Let us take that C is the top of the mountain and makes 45°with ground.

By question:

AD=1km

and /_ FAD = 30°

/_ FAC=45°

Now In ∆ ADF,

sin30° = $\dfrac{DF}{AD}$

or 1/2=DF/AD

=> 1/2=DF/1

THEREFORE DF =1/2KM

Again in ∆ DCE,

sin60°=CE/DC

=>√3/2=CE/1

THEREFORE CE =√3/2.

NOW, BC = BE+CE=DF+CE.

=[1/√2+√3/2] km

=1+1.732/2 km

=2.732/2 km

=1.366KM

$\huge\red{\boxed{HEIGHT =1.366km}}$