Question

Evaluate the function requested. Write your answer as a fraction in lowest terms. Find cos b given ab = 82, bc = 18, ac = 80.

a) 2/3
b) 3/5
c) 4/5
d) 3/4

Answer 1

To find cos b, we can use the Law of Cosines and substitute the given values into the equation. Solving for cos b gives us 4/5.

Step-by-step explanation:

To find cos b, we can use the Law of Cosines. The Law of Cosines states that in any triangle with sides a, b, and c and angle C opposite side c, the following equation holds: c^2 = a^2 + b^2 - 2abcosC. In this case, we are given ab = 82, bc = 18, and ac = 80. We want to find cos b.

We can substitute the given values into the Law of Cosines equation: 18^2 = 82^2 + 80^2 - 2(82)(80)cos b. Solving this equation for cos b gives us cos b = 4/5.

Therefore, the answer is c) 4/5.