Question

At the foot of mountain the elevation of its summit is 45°. After ascending 1km the mountain upon an inclination of 30°, the elevation changes to 60°. The height ofmountain is

Answer 1

In the figure, AB represents the mountain of height h, say. In  OCE,

sin 30° =  

cos 30° =  

OE =  

In AOB,

tan 45o =  

OA = AB

CD = EA = OA - OE = h -  

BD = AB - AD = AB - CE = h - 500

In BCD,

tan 60o =  

Thus, the height of the mountain is 1.366 km.