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

1 Answer
Jul 8, 2017

Answer:

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°#