The bearing of town C from town A is 93.3 degree if the B is 7 km from A on a bearing of 037° C is 8 km from B on a bearing of 140°
What is an angle?
When two lines or rays converge at the same point, the measurement between them is called a "Angle."
If we extend the line NA and NB
As we can see, line NA and NB are parallel and cut by transversal AB
The angle NBA and BAN' will be equal.
Angle BAN' = 180 - 37 = 143 degree = angle NBA
Angle CBA = 360 - 140 - 143
Angle CBA = 77 degree
Now, applying cos law:
b² = a² + c² - 2ac[cos B]
b² = (8)² + (7)² - 2(8 x 7 x cos77)
b = 9.37 km
To find the measure of the angle A applying sin law:
(sinA)/a = (sinB)/b
sinA = (axsinB)/b
sinA = (8xsin77)/9.37
A = 56.3⁰
Bearing of town C from town A:
α = A + 37⁰
α = 56.3⁰ + 37⁰
α = 93.3⁰
Thus, the bearing of town C from town A is 93.3 degree if the B is 7 km from A on a bearing of 037° C is 8 km from B on a bearing of 140°
Learn more about the angle here:
brainly.com/question/7116550
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