Answer:
29.7
Step-by-step explanation:
Right now you have three values:
a=45
c=23
B=36°
(note: a side is opposite of its corresponding angle in a triangle)
Since you need to find b and you have the other 2 sides and b’s corresponding angle, you use the law of cosines. The formula law of cosines, in this problem, will be:
b^2 = (a^2) + (c^2) - 2ac(cosB)
Now you just substitue in your values:
b^2 = (45^2) + (23^2) - 2(45)(23)(cos 36°)
Simplify the equation:
b^2 = 2025 + 529 - 2070(cos36°)
b^2 = 2554 - 1674.6652
b^2 = 879.3348
Now you take the square root so you can get rid of the square on b:
b = 29.7 (rounded to the nearest tenth)
