posted by Anonymous .
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
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
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
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.