What is the height of the hill if the elevation of a hill at a place due east of it is 39 degrees at a place B due south of A the elevation is 27 degrees and the distance from A to B is 500m?

Answer 1

It is not clear from the question where the point A is. This answer assumes that A is the point to the East of the hill.

Suppose the height of the hill is h metres. Suppose O is the point, on ground level, under the apex of the hill.

Then tan(39) = h/OA so that OA = h/tan(39)

Also tan(27) = h/OB so that OB = h/tan(27)

Now, triangle OAB has a right angle at A,

so by Pythagoras, OB2 = OA2 + AB2

Therefore h2/tan2(27) = h2/tan2(39) + 5002

that is h2/0.2596 = h2/0.6558 + 250000

so that 2.3269h2 = 250000

h2 = 107441

h = 327.8 metres.