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

Answer 1

tan20o = Y/X1
Y = X1*tan20.

tan10o = Y/(X1+X2).
Y = (X1+X2)*tan10
X1*tan20 = (X1+X2)*tan10
X2 = 189 Ft.
X1*tan20 = (X1+189)*tan10
X1*tan20 = X1*tan10+189*tan10
X1*tan20-X1*tan10 = 189*tan10
0.364X1-0.176X1 = 33.33
0.188X1 = 33.33
X1 = 177.3 Ft.

Y = h = X1*tan20 = 177.3*tan20=64.5 Ft.

Answer 2

NOTE: 2 rt. triangles were formed with a common vert. side and a shared hor. side(X1 and X2).