Conveyor belts called grain elevators are used to move grain into a silo. Answer the following questions knowing that the lower end of the belt is 100 feet from the base of the silo and that the silo is 150 feet tall.a. How long is the belt?b. If we know the angle of elevation from the lower end of the belt to a window on the side of the silo is 45°, use special right triangle ratios to calculate the height of the window from the ground. c. We need a ramp to the window. How long would it need to be?
a) create a right triangle using 100 for the base and 150 for the height. now find the hypotenuse, using a^2 + b^2 = c^2 100^2 + 150^2 = c^2 c = 180.28 feet
1) This is not an urgent question. This is a homework question, and it's only urgent because you put it off. 2) We will assumed, perhaps foolishly, that the silo is exactly perpendicular to the ground. That's 90 degrees. The angle of elevation is given as 45 degrees up. A triangle's inside angles always total 180 degrees, so subtract the two known angles (90 and 45 = 135) from that given (180) and find the remaining angle. You will see a familiar result. In order to have that angle at that spot, you then know that the grain elevator's height at the upper end from the bottom of the tower has to be the same as the distance of the lower end of the elevator from the bottom. The elevator itself is the hypotenuse of this big triangle, and the elevation and extension are the two legs of the right angle. In this case, having identical angles at the legs, we know then that this is, in addition to a right triangle, an isosceles triangle. Isosceles triangles have identical length legs. If you know how long one is, you know how long the other is. Answer to C: how long, indeed. A^2 + B^2 = C^2. Square the two legs, add those numbers, and find the square root of that sum. That's how long the elevator needs to be.
