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5-78.

Find the value of in each diagram below.

  1. Triangle,  Labeled as follows: left side, 17, Times, Square root of 2, left bottom angle, 45 degrees, right bottom angle, 30 degrees. Dashed line segment, from the top vertex, perpendicular to the bottom, creates 2 right triangles. Horizontal leg of right triangle on the right, labeled, x.

    Remember the side ratios for and right triangles.

  2. Triangle,  Labeled as follows: left side, x, right side, 8, left bottom angle, 45 degrees, right bottom angle, 30 degrees. Dashed line segment, from the top vertex, perpendicular to the bottom, creates 2 right triangles.

    See part (a).