Question

Can someone help me please ? I’m really struggling in this subject. Thank you

Answer 1

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
`a^(2) = b^(2) + c^(2) - 2bcCOS(A)` , but since we are finding an angle, we need to use the formula
`COS(B) = (c^(2) + a^(2) - b^(2))/(2ca)`.

With each side being the same letter as its opposite angle, so side CB would be labeled
`a` as it lies opposite angle A, we can input the values of the sides. This gives us:

`(50^(2)+ 90^(2) - 55^(2))/(2 × 50 × 90)` , which we can type into a calculator to give us the fraction
`(101)/(120)` .

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
`cos^(-1) ((101)/(120))` 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 :)