The area of a triangle is 2632 . Two of the side lengths are 85 and 63 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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The area of a triangle is 2632 . Two of the side lengths are 85 and 63 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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Area Formula: The area of a triangle can be calculated using the formula: Area = (1/2) * a * b * sin(C) where a and b are the lengths of two sides, and C is the included angle between them. We are given that the area is 2632, and the side lengths are 85 and 63. We need to find the measure of the included obtuse angle C.Plug Known Values: First, let's plug the known values into the area formula: 2632 = (1/2) * 85 * 63 * sin(C) Now, we need to solve for sin(C).Isolate sin(C): To isolate sin(C), we multiply both sides of the equation by 2 and then divide by the product of the side lengths (85 * 63): sin(C) = (2 * 2632) / (85 * 63) sin(C) = 5264 / 5355Calculate sin(C): Now, we calculate the value of sin(C): sin(C) = 5264 / 5355 sin(C) ≈ 0.9828 Since the angle is obtuse, we know that sin(C) will be positive and C will be greater than 90 degrees but less than 180 degrees.Find Angle C: To find the angle C, we need to take the inverse sine (arcsin) of sin(C). However, since the range of arcsin is typically from -90 to 90 degrees, and we know that C is obtuse, we will use the fact that sin(180° - C) = sin(C) to find the correct angle in the obtuse range.Calculate Angle C: We calculate the angle C using a calculator set to degree mode: C ≈ 180° - arcsin(0.9828) C ≈ 180° - 79.1° C ≈ 100.9°

The area of a triangle is $2632$ . Two of the side lengths are $85$ and $63$ 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 $2632$ . Two of the side lengths are $85$ and $63$ and the included angle is obtuse. Find the measure of the included angle, to the nearest tenth of $a$ degree. $\newline$ Answer: