Find the value of z
131°
x= 6.5
y= 9.4
To find the value of z, we need additional information or equations that relate z with x and y. Without that information, we cannot determine the value of z.
To find the value of z, you need to use the Law of Cosines. The formula is as follows:
c² = a² + b² - 2ab * cos(C)
Where c is the side opposite angle C.
Since x = 6.5, y = 9.4, and C = 131°, you can plug these values into the formula:
z² = x² + y² - 2xy * cos(131°)
Now, you can calculate the value of z by evaluating the equation:
z² = 6.5² + 9.4² - 2(6.5)(9.4) * cos(131°)
z² = 42.25 + 88.36 - 122.2 * cos(131°)
z² = 130.61 - 122.2 * cos(131°)
Now, compute the value of cos(131°), which is approximately -0.74805753:
z² = 130.61 - 122.2 * (-0.74805753)
z² = 130.61 + 91.45
z² = 222.06
Finally, take the square root of both sides to find the value of z:
z = √(222.06)
z ≈ 14.90