Find the area of the triangle described below. Round to the nearest hundredth.B=115°𝐵=115°, a=20𝑎=20, c=16

To find the area of a triangle when two sides and the included angle are given, we can use the formula:

Area = 1/2 * a * c * sin(B)

where: a and c are the lengths of two sides of the triangle, B is the angle included between the two sides.

Given in the problem: a = 20 c = 16 B = 115°

First, we need to convert the angle from degrees to radians because the sin function in calculators typically uses radians.

1 radian = 180/π degrees So, B = 115 * π/180 = 2.00712864 radians

Now, we can substitute these values into the formula:

Area = 1/2 * 20 * 16 * sin(2.00712864) Area = 10 * 16 * 0.906307787 Area = 144.81 square units

So, the area of the triangle is approximately 144.81 square units, rounded to the nearest hundredth.