Suppose a triangle has two sides of length 2 and 5 and that the angle between these two sides is pi/3. What is the length of the third side of the triangle?

Question

Priscilla Hayden

Mathematics

9 November, 16:45

Suppose a triangle has two sides of length 2 and 5 and that the angle between these two sides is pi/3. What is the length of the third side of the triangle?

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Melvin Pitts · Answer 1

We are given two sides of a triangle that are 2 and 5 and the angle between them is pi/3 or 60 degrees. In this case, we can use the cosine law to relate the given dimensions and angle. The cosine rule goes c2 = a2 + b2 - 2abcos C; Substituting, c2 = 4 + 25 - 2*2*5*cos pi/3; c2 = 19; c = sqrt 19 = 4.36 units.