Mathematics 10 — Exercise 7.2 · Q1 (vi)

Full question

Using the following measurements, solve triangle ABC by finding all its unknown sides and angles. If two triangles are possible, give both solutions.

Step-by-step solution

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

   $$B=180-55.0-60.0$$

2. Calculate the remaining angle.

   $$B=65.0$$

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

   $$b=\frac{6.0\times \sin \left(\mathrm{65.0°}\right)}{\sin \left(\mathrm{55.0°}\right)}$$

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

   $$b=\frac{5.4378467}{0.81915204}$$

5. Divide by the denominator sine.

   $$b=6.6383851$$

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

   $$c=\frac{6.0\times \sin \left(\mathrm{60.0°}\right)}{\sin \left(\mathrm{55.0°}\right)}$$

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

   $$c=\frac{5.1961524}{0.81915204}$$

8. Divide by the denominator sine.

   $$c=6.3433308$$

Answer

The final answer is shown below.