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 5 and the angle between sides B and C is pi/12, what are the lengths of sides A and B?

1 Answer
SCooke
Feb 18, 2018

A = B = 2.59

Explanation:

Given two angles, the third one in a triangle is fixed. In this case it is pi – 10pi/12 – pi/12 = pi/12. We have a very flat isosceles triangle.

We now have three angles and a side, and can calculate the other sides using the Law of Sines.
enter image source here
The Law of Sines (or Sine Rule) is very useful for solving triangles:
a/sin alpha = b/sin beta= c/sin gamma

Where: a, b and c are sides. alpha, beta and gamma are angles. (Side a faces angle alpha (or A), side b faces angle beta (or B) and side c faces angle gamma (or C).

And it says that: When we divide side a by the sine of angle alpha
it is equal to side b divided by the sine of angle beta,
and also equal to side c divided by the sine of angle gamma.
https://www.mathsisfun.com/algebra/trig-sine-law.html

For the given problem values: C = 5, c = 5pi/6, a = b = pi/12
5/sin (5pi/6) = A/(sin(pi/12)) = B/(sin(pi/12)) (A = B)

A = B = (sin(pi/12)) xx 5/sin (5pi/6) = 0.259 xx 10 = 2.59

Related questions
See all questions in The Law of Sines
Impact of this question
1569 views around the world
You can reuse this answer
Creative Commons License