Sine law and cosine law, including the ambiguous case
Apply the sine law or cosine law to solve a triangle, including recognizing the ambiguous (SSA) case. Unlimited questions, five difficulty levels, and a full worked solution every time — free.
Try one
A surveying crew is laying out a triangular park. Angle A = 35deg, angle B = 62deg, and the side opposite angle A is 20 m. Find the length of the side opposite angle B, to one decimal place.
Answer: 30.8
See one solved, step by step
Two hiking trails leave a lookout tower at an angle of 84deg to each other. One trail is 16 m long and the other is 10 m long. How far apart are the ends of the trails, to one decimal place?
📘 Worked solution
1c2 = p2 + q2 - 2pq·cos(C)The cosine law applies when you know two sides and the angle between them (SAS).
2c2 = 162 + 102 - 2(16)(10)cos(84deg) = 322.55Substitute the known values and simplify.
3c = √(322.55) = 18 mTake the square root and round to one decimal place.
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