Determine the angle ACB.
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here's how to solve the problem:
Part i) Calculate the distance between A and B
Step 1: Determine the angle $\angle ACB$.
The bearing of B from C is $254^\circ$.
The bearing of A from C is $344^\circ$.
The angle $\angle ACB$ is the difference between these two bearings:
$$ \angle ACB = 344^\circ - 254^\circ = 90^\circ $$
Step 2: Use the Pythagorean Theorem to find the distance AB.
Since $\angle ACB = 90^\circ$, $\triangle ABC$ is a right-angled triangle with the right angle at C.
Given $AC = 78$ m and $
