Your answer would be 32.68° to two decimal places.
When finding an angle in a triangle that does not have a right angle, and we are given all 3 sides, we can use the cosine rule.
The cosine rule to find a side is [tex] a^{2} = b^{2} + c^{2} - 2bcCOS(A) [/tex] , but since we are finding an angle, we need to use the formula [tex] COS(B) = \frac{c^{2} + a^{2} - b^{2}}{2ca} [/tex].
With each side being the same letter as its opposite angle, so side CB would be labeled [tex] a [/tex] as it lies opposite angle A, we can input the values of the sides. This gives us:
[tex] \frac{50^{2}+ 90^{2} - 55^{2}}{2 × 50 × 90} [/tex] , which we can type into a calculator to give us the fraction [tex] \frac{101}{120} [/tex] .
Because this fraction is equivalent to COS(B), we need to find the inverse of cosine so that we can get "B =", which means we do [tex] cos^{-1} (\frac{101}{120}) [/tex] and in the calculator that gives us 32.6834, or 32.68 to 2 decimal places.
I hope this helps! Let me know if you have any questions :)
