# What is the distance between the point P and the top of the pyramid?Consider a pyramid that has as its base an equilateral triangle with sides 100m each. Its three lateral faces are identical...

What is the distance between the point P and the top of the pyramid?

Consider a pyramid that has as its base an equilateral triangle with sides 100m each. Its three lateral faces are identical isosceles triangles with sides 500m each. From a point P on the ground (on the same plane as the base) the angle of elevation of the top of the pyramid is 30°. Find the distance of the point P from the top of the pyramid.

mathsworkmusic | Certified Educator

The distance from the centre of the pyramid to an apex (corner) of the base is given by

`d = 50/cos(30) = 57.7`

The height of the pyramid squared `h^2` is given by the length of one of the ridges squared minus `d_1^2`

ie, `h^2 = 500^2 - d_1^2`

`implies `  `h = sqrt(500^2 - d_1^2) = 497`

The distance of `P` from the top of the pyramid is then given by

` ``p = h/tan(30) = 860.233m`

The distance between P and the top of the pyramid is 860.233m