Mathematics 10 — Exercise Review · Q2 (iii)

Full question

Calculate the area of triangle ABC using the following measurements.

Step-by-step solution

1. Angles of a triangle sum to 180°. Subtract both known angles.

   $$B=180-44.0-36.0$$

2. Calculate the remaining angle.

   $$B=100.0$$

3. Rearrange the sine law to isolate the missing side.

   $$a=\frac{3.1\times \sin \left(\mathrm{36.0°}\right)}{\sin \left(\mathrm{44.0°}\right)}$$

4. Evaluate both sines and multiply the known side by the numerator sine.

   $$a=\frac{1.8221343}{0.69465837}$$

5. Divide by the denominator sine.

   $$a=2.6230653$$

6. Rearrange the sine law to isolate the missing side.

   $$b=\frac{3.1\times \sin \left(\mathrm{100.0°}\right)}{\sin \left(\mathrm{44.0°}\right)}$$

7. Evaluate both sines and multiply the known side by the numerator sine.

   $$b=\frac{3.052904}{0.69465837}$$

8. Divide by the denominator sine.

   $$b=4.394828$$

9. Use half the product of two sides and the sine of their INCLUDED angle.

   $$\mathrm{area}=\frac{11.527921\times \sin \left(\mathrm{44.0°}\right)}{2}$$

10. Evaluate the sine first.

    $$\sin \left(\mathrm{44.0°}\right)=0.69465837$$

11. Multiply the two side lengths.

    $$2.6230653\times 4.394828=11.527921$$

12. Multiply by the sine, then divide by 2.

    $$\frac{8.0079667}{2}$$

13. The area is in square centimetres.

    $$\mathrm{area\; (cm²)}=4.0039833$$

Answer

The final answer is shown below.