Answer: 51.5 degrees
Explanation:
The measure of the included angle is about 51.5 degrees. To find this, we can use the law of sines, which states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle. So, we can set up an equation using the information given: (area)/(0.5*(1.1)(6.6)) = (sin(x)) where x is the included angle. We know that area is 2, so we can put it in the equation: (2)/(0.5(1.1)(6.6)) = (sin(x)) .
Then using sin(x) = 2/(0.5(1.1)*(6.6)) , we can use a calculator to find the sin(x) = 0.094.
and then using a calculator, we can find that x = sin^-1 (0.094) ≈ 5.2 radians. To convert it to degrees, we can multiply it by 180/π ≈ 57.3. So the measure of the included angle is about 57.3 degrees. To the nearest tenth of a degree, it is 57.3, but it can also be rounded off to 51.5 degrees.