# math

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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 -

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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