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.
Answers
A church is 600 m due west of a flagpole. A statue is on a bearing of 160° from the church and on a bearing of 220° from the flagpole.
To find : The distance of the church from the statue.
solution : see diagram, here we put church at point C , statue at point B and flagpole at A on a line X which is parallel to Y.
from diagram, it is clear that ∠ACB = ∠ABC = 20°
so distance between flagpole and statue is 600m.
now distance between church and statue i.e., CB
here using formula,
cos140° = {AB² + AC² - BC²}/2AB AC
⇒2AB AC cos140° = AB² + AC² - BC²
⇒BC = √{AB² + AC² - 2AB AC cos140°}
= √{600² + 600² - 2 × 600² × cos140°}
= 1128 m
Therefore the distance between church and statue is 1128 m
Answer:
Step-by-step explanation:
A church is 600 m due west of a flagpole. A statue is on a bearing of 160° from the church and on a bearing of 220° from the flagpole.
To find : The distance of the church from the statue.
solution : see diagram, here we put church at point C , statue at point B and flagpole at A on a line X which is parallel to Y.
from diagram, it is clear that ∠ACB = ∠ABC = 20°
so distance between flagpole and statue is 600m.
now distance between church and statue i.e., CB
here using formula,
cos140° = {AB² + AC² - BC²}/2AB AC
⇒2AB AC cos140° = AB² + AC² - BC²
⇒BC = √{AB² + AC² - 2AB AC cos140°}
= √{600² + 600² - 2 × 600² × cos140°}
= 1128 m
Therefore the distance between church and statue is 1128 m