Question

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

Answer 1

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°`