The cosine rule - Higher
The cosine rule is: \(a^2 = b^2 + c^2 - 2bc \cos{A}\)
This version is used to calculate lengths.
It can be rearranged to: \(\cos{A} = \frac{b^2 + c^2 - a^2}{2bc}\)
This version is used to calculate angles.
Example
Calculate the length BC. Give the answer to three significant figures.
Use the form \(a^2 = b^2 + c^2 - 2bc \cos{A}\) to calculate the length.
\(\text{BC}^2 = 3^2 + 7^2 - 2 \times 3 \times 7 \cos{35}\)
\(\text{BC}^2 = 23.59561414 \dotsc\). Do not round this answer yet.
BC = 4.86 cm
Question
Calculate the angle QPR. Give the answer to three significant figures.
Use the form \(\cos{A} = \frac{b^2 + c^2 - a^2}{2bc}\) to calculate the angle.
\(\cos{y} = \frac{4^2 + 6.9^2 - 4.2^2}{2 \times 4 \times 6.9}\)
\(\cos{y} = 0.8327898 \dotsc\). Do not round this answer yet.
To calculate the angle use the inverse cos button on the calculator (\(\cos^{-1}\)).
\(y\) = 33.6掳