Mathematics 10 — Exercise Review · Q6

Full question

Hashim walks 4 km north then 3 km east. Find the bearing of his final position from the start.

Step-by-step solution

1. Take east as the horizontal component and north as the vertical component.

   $$(3,4)$$

2. Calculate this operation before combining the remaining terms.

   $$3^2=9$$

3. Calculate this operation before combining the remaining terms.

   $$4^2=16$$

4. Calculate this operation before combining the remaining terms.

   $$9+16=25$$

5. Square both components and add for the squared displacement.

   $$3^2+4^2$$

6. Take the positive square root.

   $$5.0$$

7. Find the reference angle from north/south using tan θ=|east|/|north|.

   $$\frac{3.0}{4.0}$$

8. Use inverse tangent in degrees.

   $$36.869898$$

9. Place the reference angle in its quadrant and measure clockwise from NORTH.

   $$\mathrm{bearing}=\mathrm{036.87°}$$

Answer

The final answer is shown below.