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a. Identify the parts of the handcart wheel that would represent congruent chords and congruent central angles. Explain why. b. Find the radius of the wheel. c. If the measure of the arc from to around the outside of the wheel were changed to 72°, what is the new angle the handle makes with the ground? Will the contents remain in the handcart at that angle? Will the handle rest on the ground? d. If a pioneer pulling the handcart held the handle at a height of 48 inches off the ground, would the contents of the cart spill out the back? How high can the pioneer lift the handle off the ground before the contents started spilling out?
The radius of the wheel can be found with the Pythagorean theorem. See the picture for a drawing of the triangle. 48^2 = r^2 + 45^2 48^2 - 45^2 = r^2 279 = r^2 r^2 = 279 r = sqrt(279) r = 16.703
That's for B
D. sin(angle) = opposite/hypotenuse opposite = hypotenuse sin(angle) (48-r) = 48 sin(x) (48-r) / 48 = sin(x) sin(x) = (48-r)/48 x = arcsin((48-r)/48) From part b: r = 16.703 x = arcsin((48-16.703)/48) x = arcsin((32.297)/48) x = arcsin(0.652) x = 40.694° This angle is > 20°, so the contents would spill out the back. To calculate the new height, replace the 48 with a variable and the angle x with 20°. opposite = hypotenuse sin(angle) (48-r) = 48 sin(x) Replace 48 with h. Replace x with 20°. (h-r) = 48 sin(20°) (h-16.703) = 48 sin(20°) h = 48 sin(20°) + 16.703 h = 48*0.342 + 16.703 h = 16.417 + 16.703 h = 33.120 The cart should not be lifted higher than 33 inches.
Try to get A and C
dont know how?
okay, Chord: a segment whose endpoints are on a circle. Congruent Chords: chords with equal lengths. Central Angle: angle formed from two segments that begin at the circle's center and have endpoints on the circle. Congruent Central Angles: central angles that are equal in size. If all the spokes of the wheel are an equal distance apart from each other, then every angle between them is congruent; but I think we can't assume this. If a spoke goes through the center and continues to the other side, then all the spokes are chords. They all go through the center, so they are all the same length (the diameter) and are thus, congruent to each other. Any two spokes will also form two central angles that are congruent to each other. See the picture to understand.
and that's for a
read all the questions, then the answers......this is C Lifting the handle off the ground will form a new triangle. This is still a right triangle, so one of the angles is 90° and we are told that another is 72°. We'll call the unknown angle x. The total sum of angles in a triangle is 180°. See the picture for a drawing of this new angle. 180° = 90° + 72° + x 180° - 90° - 72° = x 18° = x x = 18° The problem states: "We have to maintain the handle of the cart at an angle of no more than 20° with the ground so the contents do not spill out." The angle is 18°, so we are safe. The contents will rest in the cart at this angle and the handle is off the ground. However, if we drop the handle to the ground, the contents will probably fall out, because the larger wheel radius will allow the handle to fall down to a lower angle.
You should be able to get it from here!
thanks you guys.
No problem! Good Luck!