And the Cosine Rule: Its easier than it seems
The cosine rule has 4 variables or unknowns:
side a, side b, side c and an angle.
Or, to find an angle:
This means that if you are given 3 of those unknowns, you need to use the cosine rule.
E.g. if you are given 3 sides of a triangle (remember it should not be a right angled triangle.)
Use the cosine rule to find the angle.
Or if you are given 2 sides and the angle IN BETWEEN THOSE 2 SIDES then use the cosine rule to find the 3rd side.
Question 1: Finding a Missing Side
A triangle has sides of length 8 cm and 11 cm, with an included angle of 120°. Calculate the length of the third side to 3 significant figures.
Solution:
We use the cosine rule:
Substituting values:
Final Answer: 16.5 cm
Question 2: Finding an Angle
A triangle has sides of length 10 cm, 12 cm, and 15 cm. Find the largest angle in the triangle to 1 decimal place.
Solution:
The largest angle is opposite the longest side, so we find angle A using the cosine rule:
Substituting values:
Final Answer: 85.5°
Question 3: Word Problem – Bearings
Two boats, A and B, leave a port at the same time.
- Boat A travels 20 km due east.
- Boat B travels 25 km on a bearing of 40° from the port.
Find the distance between the two boats to 1 decimal place.
Solution:
We form a triangle where:
km km- Included angle
Using the cosine rule:
Substituting values:
Final Answer: 16.1 km
Cosine Rule Triangle Calculator - beta mode
Enter two sides and the included angle (in degrees):
More examples and practice questions coming soon!