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 :

Step-by-step solution

In ∆ C D F sin 30 ° = z 1 C D = 1   km (given) z = 1 2 ................(1) cos 30 ° = y 1 ⇒ 3 2 now in ∆ A B C tan 45 ° = h x + y ⇒ h = x + y ⇒ x = h - 3 2 .............(2) now in ∆ B D E , tan 60 ° = h - z x 3 x = h - 1 2 ⇒ 3 h - 3 2 = h - 1 2 ⇒ 3 - 1 h = 1 h = 1 3 - 1 km