The area of a triangle is 6. Two of the side lengths are 9.6 and 1.5 and the included angle is obtuse. Find the measure of the included angle, to the nearest tenth of a degree. Answer:

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Set up equation: To find the measure of the included angle, we can use the formula for the area of a triangle when two sides and the included angle are known: Area = (1/2) * a * b * sin(C), where a and b are the sides and C is the included angle. Given that the area is 6, and the sides are 9.6 and 1.5, we can set up the equation: 6 = (1/2) * 9.6 * 1.5 * sin(C)Solve for sin(C): Now we need to solve for sin(C). First, we multiply 9.6 and 1.5, then divide both sides of the equation by the result to isolate sin(C): sin(C) = (2 * 6) / (9.6 * 1.5)Calculate sin(C): Perform the calculations to find the value of sin(C): sin(C) = 12 / 14.4 sin(C) = 0.8333...Find angle C: Since the angle is obtuse, it is between 90 degrees and 180 degrees. The sine function is positive in both the first and second quadrants, but we are looking for an angle in the second quadrant (since it's obtuse). To find the angle C, we take the inverse sine (arcsin) of the value we found for sin(C). However, since arcsin will give us an angle less than 90 degrees, we need to subtract that angle from 180 degrees to find the obtuse angle. Let's first find the acute angle: C = arcsin(0.8333...)Find acute angle: Using a calculator to find the arcsin(0.8333...) gives us an acute angle. However, we need to ensure that the calculator is set to degree mode, not radian mode, to get the correct angle measurement. C_acute ≈ arcsin(0.8333...) ≈ 56.4 degreesFind obtuse angle: Now we subtract the acute angle from 180 degrees to find the obtuse angle: C_obtuse = 180 - C_acute C_obtuse = 180 - 56.4 C_obtuse = 123.6 degrees

The area of a triangle is $6$ . Two of the side lengths are $9$ . $6$ and $1$ . $5$ and the included angle is obtuse. Find the measure of the included angle, to the nearest tenth of a degree. $\newline$ Answer:

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The area of a triangle is $6$ . Two of the side lengths are $9$ . $6$ and $1$ . $5$ and the included angle is obtuse. Find the measure of the included angle, to the nearest tenth of a degree. $\newline$ Answer: