Question

A student cycle 14km east from a and then 10km south east find the distance and bearing of b from a

Answer 1

SOLUTION:

Case: Cosine rule:

Given:

Method:

Using cosine rule:

$\begin{gathered} c^2=a^2+b^2-2bc\cos C \\ c^2=10^2+14^2-2(10)(14)\cos135\degree \\ c^2=100+196-280(-0.7071) \\ c^2=296+197.99 \\ c^2=493.99 \\ c=\sqrt{493.99} \\ c=22.226 \end{gathered}$

Next, we find the bearing of B from A.

This is the angle at A

Using sine Rule:

$\begin{gathered} \frac{\sin A}{a}=\frac{\sin C}{c} \\ \frac{\sin A}{10}=\frac{\sin135}{22.226} \\ \sin A=\frac{10\times\sin135}{22.226} \\ \sin A=\frac{10\times0.7071}{22.226} \\ \sin A=0.3181 \\ A=\sin^{-1}0.3181 \\ A=18.55\degree \end{gathered}$

Final answer: To 3 and 2 decimal places

A) The distance between A and B is 22.226 hm

B) The bearing of B from A is 18.55 degrees