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Given that OB = AB, OAB is an isosceles triangle. The angles opposite the equal sides are equal, so OAB = AOB.

Mathematics

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Here's the solution for the bearing problem:

a) Calculate the bearing of B from A

Step 1: Find the angles in △OAB\triangle OAB.
Given that OB=ABOB = AB, △OAB\triangle OAB is an isosceles triangle. The angles opposite the equal sides are equal, so ∠OAB=∠AOB\angle OAB = \angle AOB.
The sum of angles in a triangle is 180∘180^\circ. We are given ∠ABO=40∘\angle ABO = 40^\circ.

∠OAB+∠AOB+∠ABO=180∘\angle OAB + \angle AOB + \angle ABO = 180^\circ

Since ∠OAB=∠AOB\angle OAB = \angle AOB, let x=∠OABx = \angle OAB.

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