7. A man finds the angle of elevation of the
top of a church spire is 30°. On walking
40 m towards the church, he finds the angle
of elevation to be 60°. Deduce the height of
the spire and his original distance from the
foot of the church.
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Answer:
BC=20
Step-by-step explanation:
In in triangle ABC
AB/BC = P/B
Tan 30=AB/BC
1/√3=AB/BD+DC
AB=BD+DC/√3. --------------------(1)
In triangle ABD
AB/BD = P/B
Tan 60 = AB/BD
√3 = AB/BD
AB=√3 BD
By 1 & 2
√3 BD = BD+DC/√3
√3(√3 BD) = BD+40
3BD = BD+40
3BD-BD=40
2BD= 40
BD=20
MAN ORIGINAL DISTANCE FROM THE FOOT OF THE CHURCH IS 20m.
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