This worksheet is about finding the length of a side using the sine rule.
Look at triangle ABC below
The sine rule states that:
|sin A||sin B||sin C|
We can use the sine rule to find an angle in the triangle when we know one other angle and the length of two sides.
Remember that, if the known angle is between the two given sides, we use the cosine rule.
In triangle PQR, which is not drawn to scale,
QR = 10 cm, PR = 12 cm and ∠PQR = 95°.
Use the sine rule to find ∠PRQ to 1 dp.
First we must find ∠QPR using the sine rule.
Using the sine rule,
|sin 95°||sin ∠QPR|
|sin ∠QPR =||10 x sin 95°|
sin ∠QPR = 0.83016...
∠QPR = sin-1 (0.83016) = 56.1°
∠PQR = 180° - 56.1° - 95° = 28.9°