Cosine law — find a side
Use the cosine law to find the third side of an acute triangle given two sides and the included angle. Unlimited questions, five difficulty levels, and a full worked solution every time — free.
Try one
Two sides of a triangular garden plot are 13 m and 12 m, with an angle of 43deg between them. Use the cosine law to find the length of the third side, to one decimal place.
c2 = a2 + b2 - 2ab·cos(C)
Answer: 9.2
See one solved, step by step
Two sides of a triangular kite frame are 22 m and 11 m, with an angle of 69deg between them. Use the cosine law to find the length of the third side, to one decimal place.
c2 = a2 + b2 - 2ab·cos(C)
📘 Worked solution
1c2 = a2 + b2 - 2ab·cos(C)The cosine law finds a side from the other two sides and the angle between them.
2c2 = 222 + 112 - 2(22)(11)cos(69deg)Substitute the known sides and included angle.
3c2 = 484 + 121 - 173.5 = 431.5Evaluate the cosine and combine the terms.
4c = √(431.5) = 20.8 mTake the square root to undo c^2.
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