A church is 600 metres due west of a flagpole. A statue is on a bearing of 160 degrees from the church and on a bearing of 220 degrees from the flagpole. Find the distance of the church from the statue.
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Answer:
A church is 600 meters due west of a flagpole. A statue is on a bearing of 160 degrees from the church and on a bearing 220 degrees from the flagpole. What is the distance of the church from the statue?
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A church is 600 meters due west of a flag pole. A statue is on a bearing of 160 degrees from the church and on a bearing of 220 degrees from the flagpole. What is the distance of the church from the statue?
Solution: The flagpole, F. is 600 m due east of the church, C.
The statue, S, has a bearing of 160 deg. from the church. So the <FCS = 160–90 = 70 deg.
The statue, S, has a bearing of 220 deg. from the flagpole. So the <FSC = 270–220 = 50 deg.
So, in the triangle FCS, <C = 70 deg., <S = 60 deg., and <F = 50 deg. FC = 600 m.
Applying the sine rule, FC/sin S = CS/Sin F, or
600/sin 60 = CS/sin 50, or
CS = 600 * sin 50/ sin 60 = 530.73 m.
The distance of the church from the statue = 530.73 m. Answer.
Step-by-step explanation:
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