In ΔRST, s = 150 inches, mm∠S=165° and mm∠T=10°. Find the length of r, to the nearest inch.

To solve this problem, 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.

The formula is: a/sinA = b/sinB = c/sinC

In this case, we know the following:

s = 150 inches ∠S = 165° ∠T = 10°

We can find ∠R using the fact that the sum of the angles in a triangle is 180°. So, ∠R = 180° - 165° - 10° = 5°.

We want to find r, which is opposite ∠R. So we can set up the following equation using the Law of Sines:

r/sin5° = 150/sin165°

Solving for r gives us:

r = (150 * sin5°) / sin165°

Using a calculator to find the sine of these angles and perform the multiplication and division gives us:

r ≈ 14.4 inches

Rounding to the nearest inch gives us r = 14 inches.