Thursday, October 7, 2010

Math problems of the week: two ways to calculate angles

I. From the "Measurements in a Right Triangle" chapter of Weeks & Atkins A Course in Geometry (1961), p. 401:

In the triangle XYZ, Z = 90o, x = .24 in., z = 12.0 in. Find angle Y.

In the triangle PQR, R = 90o, Q = 73o10', r = 12.50 ft. Find the remaining parts of the triangle.

A triangle has sides 10.0 in, 10.0 in., 8.25 in. long. Find the size of the smallest angle. 

II. From the "Triangles and Trigonometric Ratios" chapter of Contemporary Mathematics in Context Course 2, part B (2003), p. 403:

Suppose you know sin A = 4/5 = .8 Use the sin-1 function of your calculator to compute the angle whose sine is 0.8. (Make certain your calculator is set in degree mode.)

Use your calculator to find the measure of the angle in each of the following cases.

tan B = 1.84
sin A = 0.852
cos B = 0.213

III. Extra Credit

Discuss the possible connection between spelling out that 4/5 = .8 and telling students to use their calculators.

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