How do you find the angles of a triangle given sides 9, 6, and 14?

1 Answer
EZ as pi
Jul 8, 2017

The angles are 137°, 26° and 17°

Explanation:

Firstly, Is it a right-angled triangle?
Check using Pythagoras's Theorem.
6^2 +9^2 = 117" and "14^2 = 196
No 90° angle, but the biggest angle will be obtuse because the square of the longest side is bigger than the sum of the squares of the other 2 sides.

Use the Cosine rule to find the biggest angle first - that will tell you whether the angle is acute or obtuse.

Cos theta = (6^2+9^2-14^2)/(2xx6xx9) = -0.73148
theta = 137°

Now use the Sine rule:

(Sin beta)/9 = (sin137)/14

sin beta = (9sin137)/9 = 0.438339
beta = 26°

Use the sum of the angles to find the third angle:

gamma = 180°-137°-26° =17°

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