to find the height

Let the horizontal distance of the summit and mountain foot be X, and height of mountain be H.

tan 45 = H/X

X = H

Ascending a distance of 1.5 km along the inclination of 30, means travelling a distance x horizontally, so that

cos 30 = x/1.5

x = 33/4

So the horizontal distance between the summit and observer is now X - x or X - 33/4.

Similarly by travelling along the incline we travelled a distance x horizontally and so a distance h vertically.

sin 30 = h/1.5

h = 3/4

And now the angle of elevation is 60.

So

tan 60 = (H - h)/(X - x) = (H - 3/4)/(H - 33/4)...................since H = X

3H - 9/4 = H - 3/4

(3 - 1)H = 3/2

H = 3/2(3 - 1) = 2.05 km

Regards,

Team,

TopperLearning.