A triangle has sides A, B, and C. The angle between sides A and B is (5pi)/6. If side C has a length of 2 and the angle between sides B and C is pi/12, what are the lengths of sides A and B?

1 Answer
jim p. ยท Shwetank Mauria
Oct 24, 2017

A = B = 1.035

Explanation:

This one is deceptively easy, I think.

You know that the interior angles of a triangle add up to pi radians (or 180 degrees). You are given 2 of the angles, so you can calculate the angle between sides A and C = pi - (pi/12 + (5pi)/6)

...this comes out to pi/12. This is the same as the angle between sides B & C.

So you know you have an isosceles triangle, and therefore sides A and B are equal.

From your equilateral triangle, you can create two congruent right triangles, with hypotenuse A (or B), and base of length C_1 and C_2. (C_1 + C_2 = 2, and since the two right triangles are equal, C_1 = C_2, so C_1 = C_2 = 1)

So now, using just a little trig, we know: C_1/A = cos(pi/12)
...since C_1 = 1, we have 1/A = cos(pi/12)
Therefore, A = 1/cos(pi/12)

A = 1.035 (rounding)

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