This worksheet is about finding angles using the cosine rule.
Look at triangle ABC below
The cosine rule states that:
a2 = b2 + c2 - 2bc cosA
We can use the cosine rule to find an angle when we know all three sides of a triangle.
The side of length a will be opposite the angle we are trying to find.
In triangle PQR, which is not drawn to scale,
PQ = 9 cm, QR = 10 cm, and PR = 15 cm.
Use the cosine rule to find ∠PQR to the nearest degree.
Using the cosine rule,
152 = 92 + 102 - 2 x 9 x 10 x cosθº
225 = 81 + 100 - 180cosθº
180cosθº = 81 + 100 - 225 = -44
cosθº = -44 ÷ 180 = -0.24444444....
θº = cos-1(-0.24444444...) = 104°