Answer: 016T (don’t forgot the degrees symbol between 6 and T)
Let’s express that problem into a diagram for visualisation purposes. In this case, finding the true bearing directly back to point A is denoted by theta.
How can we find theta. Well notice that we can create a right angle triangle. We know that the sum of the angles inside the triangles add up to 180 degrees. Since the triangle we created is a right angled one, we know one of the angles is 90 degrees for sure. So we only need one more angle to go and do some algebra to find theta.
Now we know that the boat sailed on a true bearing of 196 degrees. Let’s split that so that we can create a supplementary angle with x. Since one quarter is 90, that means the other remaining angle will be 106 degrees:
X + 106 = 180 (supplementary)
X = 74
There’s our second angle. Now let’s solve for theta.
180 = 74 + 90 + θ (angle sum in triangle)
180 = 164 + θ
180 - 164 = 180 - 164 + θ (isolate θ by subtracting 164 from both sides; since we do it to both sides, it does not imbalance the equation)
θ = 16
