Given ABC with a = 22, b = 26, and mC 72° , find c. Round the cosine value to the nearest thousandth and answer to the nearest hundredth.
I got 28.40
That's what I got.
To find the length of side c in a triangle, you can use the Law of Cosines, which states that:
c^2 = a^2 + b^2 - 2ab * cos(C)
In this case, we have a = 22, b = 26, and C = 72°. Let's calculate c using this formula:
c^2 = 22^2 + 26^2 - 2 * 22 * 26 * cos(72°)
Now, calculate the cosine of 72°:
cos(72°) ≈ 0.309 (rounded to the nearest thousandth)
Now substitute this value into the equation:
c^2 = 22^2 + 26^2 - 2 * 22 * 26 * 0.309
Simplify:
c^2 = 484 + 676 - 1143.552
c^2 = 16.448
Now, take the square root of both sides to solve for c:
c ≈ √16.448
c ≈ 4.064 (rounded to the nearest hundredth)
Therefore, the length of side c is approximately 4.06 (rounded to the nearest hundredth), not 28.40.