Question

A triangle has sides A, B, and C. Sides A and B are of lengths `11` and `12`, respectively, and the angle between A and B is `(5pi)/8`. What is the length of side C?

Answer 1

≈ 19.13

Explanation:

In a triangle , given 2 sides and the angle between them, to find the 3rd side use the `color(blue)" cosine rule "`

`color(red)(|bar(ul(color(white)(a/a)color(black)( c^2 = a^2 + b^2 - (2abcosC))color(white)(a/a)|)))`

where a , b are the 2 known sides and angle C , is the angle between them.
here a = 11 , b = 12 and angle C = `(5pi)/8`

substituting these values into the formula

`c^2 = 11^2 + 12^2 - ( 2xx11xx12xxcos((5pi)/8) )`

`= 121 + 144 - ( -101.03) = 366.03`

now `c^2 = 366.03 rArr c = sqrt366.03 ≈ 19.13`