# At the foot of the mountain, the elevation of its summit is 45°, after ascending 1000m towards the mountain up a slope of 30°, inclination the elevation found to be 60°. Find the height of the mountain.

The figure is given below:

height of mountain = CD = H

In ΔACD,

DC = AC = H

In ΔEAB,

y

Thus, BC = AC – AB = (H–500)m

AB = 500√3m

thus BC = AC – AB = (H – 500√3)m

thus EF = (H–500√3)m (since BC = EF)

In ΔDEF,

H = 1350 m

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