Functions (MCR3U) · Trigonometric Functions

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, included free with weekly lessons.

Practice this skill Curriculum: MCR3U-TF1.3

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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