Assignment #88: Solving More Right Triangles
Problems
1. Use the definitions and any right triangle to show the following:
sin x
a. cos x = tan x
b. (sin x)2 + (cos x)2 = 1
c. sin x = cos(90-x) d. cos x = sin(90-x)
Solve each right triangle (find all the sides and angles that are not numerically given).
2.
3.
4.
5.
6. Find x. (Yes, these are right triangles.)
a.
b.
(R):
(L): A set of numbers has a mode of 32, a median m, and a mean of 22. The smallest number is 10. If
m is increased to m+10, the mean becomes 24. If m is decreased to m-8, the mean becomes m-4. Find
m.
See R. problem next page.
(R): Sandy’s Sandbox Sand Co. has one plant in Seattle and one in Portland. At the moment, the
company has a total 100 cubic feet of sand in stock, 80 cubic feet in Seattle and 20 cubic feet in
Portland. Suddenly, all of the sand is needed because orders come in from Spokane, Goldendale, and
Longview. Spokane wants 40 cubic feet, Goldendale wants 50 cubic feet, and Longview wants the
remaining 10 cubic feet. Sandy has a problem because it costs roughly 10 cents per cubic foot per mile
to transport sand, and she wants to deliver the sand in the cheapest possible way. She hires you to fill in
the following shipping table so as to minimize costs.
Route
Distance (miles)
Amount to transport
Seattle to Spokane
Seattle to Goldendale
Seattle to Longview
Portland to Spokane
Portland to Goldendale
Portland to Longview
280
212
126
351
118
48
____________
____________
____________
____________
____________
____________
(Hint: let x be the amount to be transported from Seattle to Spokane and y be the amount to be shipped
from Seattle to Goldendale. All the other amounts can be expressed in terms of x or y.)