Answer:
a. 33.01
Explanation:
Since we don't know whether or not triangle ABC is a right angle and we have an angle sandwiched between two sides, we can find the length of BC using the Law of Cosines, which is given by:
a^2 = b^2 + c^2 - 2bc * cos A
b^2 = a^2 + c^2 - 2ac * cos B
c^2 = a^2 + b^2 - 2ab * cos C
We can call let A represent angle A, c represent side AB, let b represent side AC, and let a represent side BC.
Thus, we can find the length of a (i.e., BC) using the first equation from the law of cosines:
Step 1: Plug in 91 for A, 28 for c, and 17 for b and simplify:
a^2 = 17^2 + 28^2 - 2(17)(28) * cos (91)
a^2 = 1073 - 952 * cos (91)
Step 2: Take the square root of both sides to solve for a (i.e., the length of side BC) and round:
Note that since we want a positive answer, we can already ignore the negative answer to the square root:
√(a^2) = √(1073 - 952 * cos (91))
a = 33.00931219
a = 33.01
Thus, side BC is about 33.01 units long.