Question

A, B, and C are the locations of three support posts. The bearing from post B to post A is 45degrees. The bearing from post A to post C is 135degrees. If AB= 8 meters and AC= 6 meters, what is the bearing to post B from post C?

Answer 1

Check the picture below.

make sure your calculator is in Degree mode.

Answer 2

53.06°

Explanation:

In triangle ABC, since ∠CAB is 90 degree, therefore consider AB to be the opposite and AC be the adjacent.

Now to find the angle, ∠ACB using trigonometry,

tan θ = opposite / adjacent

tan θ = AB / AC

given AC = 6 and AB = 8

tan θ = 8 / 6

tan θ = 1.33

therefore, θ =
`tan^(-1)` 1.33

θ = 53.06°

Therefore, the bearing from post C to post B is 53.06°