Posted by **Anonymous** on Saturday, April 6, 2013 at 12:57am.

the angle of elevation from point on the ground to the top of a pyramid is 20 degrees 20 degrees the angle elevation from a point 189 feet farther back to the top of the pyramid is 10 degrees 20 degrees. find the height of the pyramid

- math -
**MathMate**, Saturday, April 6, 2013 at 8:54am
Let A be the top of the pyramid,

B = centre of pyramid at ground level

P=position of first observation (angle=20 deg)

Q=position of second observation (angle=10 degrees)

Then PQ=189 feet

and APQ is a triangle where

APQ=10°

AQP=180-20=160°

Consequently PAQ=10 deg by angles of a triangle.

Since triangle PAQ is an isosceles triangle, we deduce that PA=189 feet.

and the height of the pyramid is

h=189sin(20 deg).

Note:

This solutions takes advantage of the fact that the triangle is isosceles.

In general, if it is not, the triangle can be solved using the sine rule, and h found consequently.

If you have not done sine rule already, then you can let h=AB, and x=PB.

Form two equations using each of the triangles APB and AQB in terms of h and x. Solve for h by eliminating x.

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