An oblique triangle has sides of 17 cm and 28 cm. If the included angle measures 91 degrees, then what is the measure of the side opposite that angle? Round to the nearest whole number.(1 point)
To find the side opposite the angle, we can use the Law of Cosines. The formula is given by:
c^2 = a^2 + b^2 - 2ab*cos(C)
Where a and b are the given sides of the triangle and C is the included angle.
Plugging in the values, we get:
c^2 = 17^2 + 28^2 - 2 * 17 * 28 * cos(91°)
Simplifying this equation gives:
c^2 = 289 + 784 - 2 * 17 * 28 * cos(91°)
c^2 = 289 + 784 - 9578 * cos(91°)
Using a calculator to evaluate the cosine of 91°, we find that cos(91°) is approximately -0.44807362.
Substituting this value in the equation gives:
c^2 = 289 + 784 - 9578 * (-0.44807362)
c^2 = 289 + 784 + 4293.91928
c^2 = 4366.91928
To find c, we need to take the square root of both sides:
c = √4366.91928
c ≈ 66.10
Rounding to the nearest whole number, the measure of the side opposite the angle is 66 cm.