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The length of the hypotenuse is 10 3.

h = 2 • 5 6 hypotenuse = 2 • leg. h = 5 12 Simplify. h = 5 4(3). h = 5(2) 3. h = 10 3. The length of the hypotenuse is 10 3. Special Right Triangles. LESSON 8-2. Additional Examples.

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The length of the hypotenuse is 10 3.

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  1. h = 2 •5 6 hypotenuse = 2 • leg h = 5 12 Simplify. h = 5 4(3) h = 5(2) 3 h = 10 3 The length of the hypotenuse is 10 3. Special Right Triangles LESSON 8-2 Additional Examples Find the length of the hypotenuse of a 45°-45°-90° triangle with legs of length 5 6. Use the 45°-45°-90° Triangle Theorem to find the hypotenuse.

  2. 22= 2 • leg hypotenuse = 2 • leg 22 2 x = Divide each side by 2. 22 2 2 2 x = • Simplify by rationalizing the denominator. x = 22 2 2 x = 11 2 Simplify. The length of the leg is 11 2. Special Right Triangles LESSON 8-2 Additional Examples Find the length of a leg of a 45°-45°-90° triangle with a hypotenuse of length 22. Use the 45°-45°-90° Triangle Theorem to find the leg.

  3. 96= 2 • leg hypotenuse = 2 • leg 96 2 leg = Divide each side by 2. leg = Use a calculator. Special Right Triangles LESSON 8-2 Additional Examples The distance from one corner to the opposite corner of a square playground is 96 ft. To the nearest foot, how long is each side of the playground? The distance from one corner to the opposite corner, 96 ft, is the length of the hypotenuse of a 45°-45°-90° triangle. Each side of the playground is about 68 ft.

  4. 18= 3 • shorter leg longer leg = 3 • shorter leg d = Divide each side by 3. 3 3 18 3 d = • Simplify by rationalizing the denominator. d = 18 3 3 d = 6 3 Simplify. f = 2 • 6 3hypotenuse = 2 • shorter leg 18 3 f = 12 3 Simplify. The length of the shorter leg is 6 3, and the length of the hypotenuse is 12 3. Special Right Triangles LESSON 8-2 Additional Examples The longer leg of a 30°-60°-90° triangle has length 18. Find the lengths of the shorter leg and the hypotenuse. You can use the 30°-60°-90° Triangle Theorem to find the lengths.

  5. Special Right Triangles LESSON 8-2 Additional Examples A garden shaped like a rhombus has a perimeter of 100 ft and a 60° angle. Find the perpendicular height between the two bases. Because a rhombus has four sides of equal length, each side is 25 ft. Draw the rhombus with altitude h, and then solve for h.

  6. 25 2 shorter leg = = 12.5 Divide each side by 2. h = 12.5 3 longer leg = 3 • shorter leg Special Right Triangles LESSON 8-2 Additional Examples (continued) The height h is the longer leg of the right triangle. To find the height h, you can use the properties of 30°-60°-90° triangles. 25 = 2 • shorter leg hypotenuse = 2 • shorter leg h ≈ 21.65 The perpendicular height between the two bases is about 21.7 ft.

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