A.) The diameter of a Ferris wheel is 217 feet. The top of the wheel stands 230

Question

A.) The diameter of a Ferris wheel is 217 feet. The top of the wheel stands 230 feet above the ground. The figure below is a model of the Ferris wheel with angle the central angle that is formed as a rider moves from the initial position P0 to position P1. The rider is h feet above the ground at position P1. (Round your answers to the nearest whole number.)

Find h if is 120.0°, 210.0°, and 315.0°.

B.)Suppose each edge of the cube shown in the figure is x inches long. Find the measure of the angle formed by diagonals DE and DG. Round your answer to the nearest tenth of a degree.

C.)The circle in the figure below has a radius of r and center at C. The distance from A to B is x. Redraw the figure below, label as indicated in the problem, and then solve the problem.

If C = 61° and x = 23, find r. (Round your answer to the nearest whole number.)

Explanation / Answer

2) length of edge = x inches

| DG | = sqrt ( x^2 + x^2 ) = sqrt ( 2x^2 ) = x sqrt 2

tan EDG = EG / GD = x / xsqrt 2 = sqrt 2 / 2

EDG = tan-1 ( sqrt 2 / 2 )

EDG = 45 degrees

c) angle C = 61 degrees

taking the right angle triangle CDA

we can write

cos 61 = base / hypotenuse

base = r

hypotenuse = r + x = r + 23

therefore,

cos 61 = r / ( r + 23 )

.4848 = r / ( r + 23 )

multiplying both sides by ( r+ 23 )

.4848r + 11.15 = r

on solving we get

r = 11.15 / .5152

r = 21.64

r = 22 ( round off )

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