Mathematics 10 — Exercise Review · Q3 (ii)

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.

   $$B=180-32.0-48.0$$

2. Calculate the remaining angle.

   $$B=100.0$$

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

   $$a=\frac{81.0\times \sin \left(\mathrm{32.0°}\right)}{\sin \left(\mathrm{48.0°}\right)}$$

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

   $$a=\frac{42.92346}{0.74314483}$$

5. Divide by the denominator sine.

   $$a=57.759213$$

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

   $$b=\frac{81.0\times \sin \left(\mathrm{100.0°}\right)}{\sin \left(\mathrm{48.0°}\right)}$$

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

   $$b=\frac{79.769428}{0.74314483}$$

8. Divide by the denominator sine.

   $$b=107.34035$$

Answer

The final answer is shown below.