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Contents Lesson 7-1Geometric Mean Lesson 7-2The Pythagorean Theorem and Its Converse Lesson 7-3Special Right Triangles Lesson 7-4Trigonometry Lesson 7-5Angles of Elevation and Depression Lesson 7-6The Law of Sines Lesson 7-7The Law of Cosines
Lesson 3 Contents Example 1Find the Measure of the Hypotenuse Example 2Find the Measure of the Legs Example 330°–60°–90° Triangles Example 4Special Triangles in a Coordinate Plan
Example 3-1a WALLPAPER TILING The wallpaper in the figure can be divided into four equal square quadrants so that each square contains 8 triangles. What is the area of one of the squares if the hypotenuse of each 40°-45°-90° triangle measures millimeters?
Example 3-1b The length of the hypotenuse of one 40°-45°-90° triangle is millimeters. The length of the hypotenuse is times as long as a leg. So, the length of each leg is 7 millimeters. The area of one of these triangles is or 24.5 millimeters. Answer: Since there are 8 of these triangles in one square quadrant, the area of one of these squares is 8(24.5) or 196 mm 2.
Example 3-1c WALLPAPER TILING If each 40°-45°-90° triangle in the figure has a hypotenuse of millimeters, what is the perimeter of the entire square? Answer: 80 mm
Example 3-2a Find a. The length of the hypotenuse of a 40°-45°-90° triangle is times as long as a leg of the triangle.
Example 3-2b Multiply. Divide. Rationalize the denominator. Divide each side by Answer:
Example 3-2c Find b. Answer:
End of Lesson 3
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