Cosine law
Use the cosine law to find a missing side or angle in an acute triangle, including a surveying word problem. Unlimited questions, five difficulty levels, and a full worked solution every time — free.
Try one
Two hiking trails leave a lookout tower at an angle of 75deg to each other. One trail is 29 m long and the other is 28 m long. How far apart are the ends of the trails, to one decimal place?
Answer: 34.7
See one solved, step by step
A triangular garden has sides a = 9 m, b = 8 m, and c = 2 m. Find the measure of angle C (opposite side c), to the nearest degree.
📘 Worked solution
1cos(C) = (a2 + b2 - c2)/(2ab)Rearranging the cosine law lets you solve for an angle when you know all three sides.
2cos(C) = (92 + 82 - 22)/(2·9·8) = 0.9792Substitute the three side lengths and simplify.
3C = cos-1(0.9792) = 12degApply inverse cosine and round to the nearest degree.
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