When we start on this problem, let's go to the home key and let's make sure that our settings are correct. So #5 document settings number two, we want to be in degree mode, and we are. I'm going to make it the default. I'm going to start a new document. I'm not going to save the old one, and I'm going to add a calculator. So when we look at this problem, it talks about having this cone and having things fall and the cone getting bigger. It gives us this equation that Theta equal cotangent inverse of r / H when certain granular materials are stored in a pile 17 feet high. So we know our height the 17 and we know that our diameter is 25 if our diameter is 25. Remember diameter is really just to radius. So if I know my diameter is 25 I can get my radius is 25 / 2 which is 12.5. Looking at this triangle Now I can realize I can find this Theta value because tangent Theta is going to be 17 / 12.5 or Theta is just going to be tangent inverse of 17 / 12.5. So if we go to our calculator and we go to our tangent inverse of 17 / 12.5, I'm going to do control and enter to get an approximate. So 53.67 approximately, which is what it has here. When we round to two decimal places then it says what's the base diameter of a pile that's 15 feet high. So now we have a height, the 15 and we need the R. We know the Theta because the Theta is going to be the same as what we found previously. So now we can say cotangent Theta is adjacent over hypotenuse and I put the adjacent on top because that was the unknown I'm solving for. So then if I cross multiply, I get my 15 times cotangent Theta equaling R. Now remember R is half of the diameter, so we need 2R S to be the full diameter. So I just multiplied each side by two. So this is going to tell me my diameter is 30 cotangent Theta. So when I go back to my calculator, I'm going to type in 30 and we can type in cotangent. Actually, let's just do that cot on our calculator COT. If I put a parenthesis, I can then go up and just grab that angle by hitting enter and then control enter again to get my answer of 22.06. So 22.06, that was Part B Part C says what's the height of pile whose base diameter is 114 feet. So if the diameter is 114 feet, half the diameter is 57. We're wanting to find the height. So we need opposite over adjacent and we want the opposite on top because that's our unknown. So tangent Theta is H / 57. I just cross multiplying it 57 tangent Theta equaling H So if I go into my calculator 57 tangent and I can grow up and up and up to grab that Theta, I just arrow up and control enter to get 77.52.