Question

A triangle has sides A, B, and C. Sides A and B are of lengths `5` and `6`, respectively, and the angle between A and B is `(5pi)/12`. What is the length of side C?

Answer 1

c = 6.74 ( 2 decimal places )

Explanation:

I recommend that you draw a sketch of the triangle where you will see that we are given 2 sides and the included angle ie. the angle between the 2 given sides.

For this condition to find the third side use the cosine rule

`color(red)( c^2 = a^2 + b^2 - ( 2ab cos c )`

here `a = 5 , b =6 and c =( 5pi) / 12`

substitute these values into the cosine rule

`rArr c^2 = 5^2 + 6^2 - ( 2 xx 5 xx 6 xx cos((5pi)/12 )`

evaluating : `c^2 = 25 + 36 - 15.529`

`rArr c^2 = 45.471`

At this stage remember to take the square root to get c.

`rArr c = 6.74` ( 2 decimal places )