Answer:
1. The distance from the base camp is 37 Km
2. The bearing from the base camp is 72°
Step-by-step explanation:
Please see attached photo for explanation.
1. Determination of the distance from the base camp.
In the attached photo, x is the distance from the base camp. The value of x can be obtained by using the cosine rule formula. This is illustrated below:
Side opposite A = a = 28 Km
Side opposite C = c = 43 Km
Angle B = 58°
Side opposite B = b = x =?
b² = a² + c² – 2ac Cos B
x² = 28² + 43² – 2 × 28 × 43 Cos 58
x² = 784 + 1849 – 2408 × 0.52991
x² = 2633 – 1276
x² = 1357
Take the square root of both side
x = √1357
x ≈ 37 Km
Thus, the distance from the base camp is 37 Km.
2. Determination of the bearing from the base camp
We'll begin by calculating the value of θ in the attached photo. This can be obtained by using sine rule formula as shown below:
Side opposite A = a = 28 Km
Side opposite B = b = x = 37
Angle B = 58°
Angle A = θ =?
a/Sine A = b/SineB
28/Sine θ = 37/Sine 58
Cross multiply
37 × Sine θ = 28 × Sine 58
Divide both side by 37
Sine θ = 28 × Sine 58 /37
Sine θ = 28 × 0.8480 / 37
Sine θ = 0.6417
Take the inverse of sine
θ = Sine¯¹ 0.6417
θ = 40
Finally, we shall determine the bearing from the base camp. This can be obtained as follow:
Bearing from the base camp = 32 + θ
θ = 40
Bearing from the base camp = 32 + 40
Bearing from the base camp = 72°
