from a particular point the angle of elevation of the top of a church spire is 35 degrees. walking 30 metres closer to the church the angle of elevation of the top of the spire increases by 20 degrees.
a. how far from the church was the second elevation taken?
b. calculate the height of the church spire.
Did you make a sketch?
on mine, I labeled the original point A, and the closer point B. Top of the church P, bottom of church Q
AB = 30, angle A = 35°, angle PBQ = 55°
in triangle PAB, angle PBA = 125°, then
angle APB = 20°
by the sine law:
BP/sin35 = 30/sin20
BP = 30sin35/sin20 = ....
now in the right-angled triangle PBQ , you have the hypotenuse BP and an angle, you can now find PQ
PQ/PB = sin 55°
PQ = PBsin55°
hint: your display should still display the answer for BP. Just enter
x sin55 =