In ΔKLM, l = 170 inches, m = 210 inches and ∠K=46°. Find the area of ΔKLM, to the nearest square inch.

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

Area = 1/2 * a * b * sin(C)

where a and b are the lengths of the two given sides, and C is the measure of the included angle.

In this case, a = l = 170 inches, b = m = 210 inches, and C = ∠K = 46°.

First, convert the angle from degrees to radians because the sin function in most calculators uses radians. To convert from degrees to radians, multiply by π/180. So, C = 46 * π/180 = 0.80285 radians.

Then, substitute these values into the formula:

Area = 1/2 * 170 inches * 210 inches * sin(0.80285 radians)

Calculate the value:

Area ≈ 1/2 * 170 * 210 * 0.71934 ≈ 12732.5 square inches

So, the area of ΔKLM is approximately 12733 square inches, to the nearest square inch.