Answer:
b ≈ 29.7 units
Explanation:
Because we don't know whether this is a right triangle, but have an angle sandwiched between two sides, we can use the law of cosines to find b.
The law of cosines is given by the following formula:
(1.) a^2 = b^2 + c^2 - 2bc * cos(A)
(2.) b^2 = a^2 + c^2 -2ac * cos(B)
(3.) c^2 = a^2 + b^2 - 2ab * cos(C)
Because angle B is sandwiched between a and c, we can use formula 2 by plugging in 45 for a, 23 for c, and 36 for B.
Step 1: Plug everything in and simplify:
b^2 = a^2 + c^2 -2ac * cos(B)
b^2 = 45^2 + 23^2 - 2(45)(23) * cos(36)
b^2 = 2025 + 529 - 2070 * cos(36)
b^2 = 2554 - 2070 * cos(36)
b^2 = 879.3348216
Step 2: Take the square root of both sides to find b and then round to the nearest tenth:
√b^2 = ± √879.3348216
b = 29.65358025
b = 29.7
Although taking the square root of number gives you a positive and negative number since squaring both a positive and negative number give you a positive answer (e.g., 2 * 2 = 4 and -2 * -2 = 4), we can only use the positive answer since you can't have a negative measure. Thus, b is approximately 29.7 units.