Final answer:
In the triangle with sides 5.58, 15.2, and 9.14, and with angle A measuring 65 degrees, the value of x is approximately 13.810 units.
Step-by-step explanation:
Let's find the value of x in the triangle with sides 5.58, 15.2, and 9.14, assuming that angle A is 65 degrees.
To solve this, we can use the Law of Cosines, which states that in a triangle with sides a, b, and c, and angle C opposite side c, the following equation holds:
c² = a² + b² - 2ab*cos(C).
In our triangle, side c is the unknown side (x), side a is 5.58, side b is 15.2, and angle C is opposite side c. We also know that angle A is 65 degrees.
1. Substitute the known values into the Law of Cosines equation:
x²= 5.58²+ 15.2² - 2 * 5.58 * 15.2 * cos(65)
2. Evaluate the expression:
x²= 31.1364 + 231.04 - 169.344 * cos(65)
3. Calculate the cosine of 65 degrees using a calculator:
cos(65) ≈ 0.4226
4. Substitute the value of cos(65) into the equation:
x² = 31.1364 + 231.04 - 169.344 * 0.4226
5. Simplify the equation:
x² ≈ 31.1364 + 231.04 - 71.6005
x²≈ 190.5759
6. Take the square root of both sides to solve for x:
x ≈ √190.5759
x ≈ 13.810
Therefore, in the triangle with sides 5.58, 15.2, and 9.14, and with angle A measuring 65 degrees, the value of x is approximately 13.810 units.