Posted by Anonymous on .
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,
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=18020=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.