The angle of elevation of the summit of a mountain from a point on the ground is 45 ° . After climbing…

The angle of elevation of the summit of a mountain from a point on the ground is 45°. After climbing up one km towards the summit at an inclination of 30° from the ground, the angle of elevation of the summit is found to be 60°. Then the height (in km) of the summit from the ground is :
  1. 3-13+1
  2. 3+13-1
  3. 13-1
  4. 13+1

Solution

  

In∆CDF

sin30°=z1CD=1 km

(given)

z=12   ................(1)

cos30°=y1⇒32

now in

∆ABC

tan45°=hx+y

⇒h=x+y

⇒x=h-32 .............(2)

now in

∆BDE,

tan60°=h-zx

3x=h-12⇒3h-32=h-12⇒3-1h=1

h=13-1km

Asked in: JEE Main 2020 (06 Sep Shift 2)

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