The bearing of town C from town A at the given position of the three towns is determined as 93.3⁰.
Distance of C from A
The distance of town C from town A is calculated by applying Cosine rule. The distance of town C from town A is represented by small letter "b" as shown in the image.
b² = a² + c² - 2ac[cos B]
b² = (8)² + (7)² - 2(8 x 7 x cos77)
b² = 87.81
b = √87.81
b = 9.37 km
Angle A
The value of angle A is determined by applying Sine rule as shown below;
sin A/a = sin B/b
sin A = (a x sin B)/b
sin A = (8 x sin 77)/9.37
sin A = 0.832
A = sin ⁻¹ (0.832)
A = 56.3⁰
Bearing of town C from town A
The bearing of town C from town A is determined from the sum of 37⁰ and angle A.
θ = A + 37⁰
θ = 56.3⁰ + 37⁰
θ = 93.3⁰
Thus, the bearing of town C from town A at the given position of the three towns is determined as 93.3⁰.
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