Tangent Theta is going to equal the building height 55 over the shadow X. If we take the derivative of each side in terms of time, we get secant square Theta D Theta DT equaling -55 / X ^2 DX DT. Now we're trying to solve for the shadow, so the rate of the shadows. So we're going to take that -55 / X ^2 to the other side and get negative X ^2 / 55 secant squared Theta D Theta DT equaling DXDT. They want to know what's happening when X when the shadow is 132. So if we look at our triangle and we have a height of 55 and we have a shadow of 132, we can find the hypotenuse because we know two sides of a right triangle and we get 143. So the secant of this triangle is going to be hypotenuse over adjacent or 143 / 132 ^2. The D Theta DT was given as .27° per minute and it tells us to remember to use radians in our calculation. So we need to change that degrees to radians by multiplying by π / 180. When we do that, we get -1.75 two O 7 feet per minute. But if we look at what the answer is being asked, it's asking us for inches per minute. So we're going to multiply by 12 inches in a foot, so the feet and top and bottom cancel, and we're going to get -21.025 for the change of the shadow. In terms of time. When the shadow is 132, the directions asks us to round A1 decimal place as needed. So we'd have two 1.0 or 21. The shadow is decreasing, so that takes enough to account the negative portion.