At the foot of the mountain, the angle of elevation of its summit is 45 o , after ascending 1000   m towards the mountain up a slope of 30 o inclination, the angle of elevation is found to be 60 o . The height (in km ) of the mountain is (take 3 = 1 .7 )

Step-by-step solution

Let P be the summit of the mountain and Q be the foot. Let A be the first position and B the second position of observation. B N and B M are ⊥ s from B to P Q and A Q respectively. Then, A B = 1000 m = 1 k m , ∠ M A B = 30 o , ∠ M A P = 45 o , ∠ N B P = 60 o Now, ∠ B A P = ∠ M A P - ∠ M A B = 45 o - 30 o = 15 o ∠ A P B = ∠ A P N - ∠ B P N = 45 o - 30 o = 15 o ∴ ∆ A B P is isosceles ∴ A B = B P But, A B = 1 kilometre ∴ B P = 1 kilome