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8-3 Special Right Triangles

8-3 Special Right Triangles. Special Right Triangles. GEOMETRY LESSON 8-2. (For help, go to Lesson 1-6.). 1. 2. 3. Use a protractor to find the measures of the angles of each triangle. Check Skills You’ll Need. 8-3. Special Right Triangles. GEOMETRY LESSON 8-2. Solutions.

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8-3 Special Right Triangles

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  1. 8-3 Special Right Triangles

  2. Special Right Triangles GEOMETRY LESSON 8-2 (For help, go to Lesson 1-6.) 1.2. 3. Use a protractor to find the measures of the angles of each triangle. Check Skills You’ll Need 8-3

  3. Special Right Triangles GEOMETRY LESSON 8-2 Solutions 1. 45, 45, 90 2. 30, 60, 90 3. 45, 45, 90 8-3

  4. Special Right Triangles Find the length of the hypotenuse of a 45°-45°-90° triangle with legs of length 5 6. 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. GEOMETRY LESSON 8-2 Use the 45°-45°-90° Triangle Theorem to find the hypotenuse. Quick Check 8-3

  5. Special Right Triangles Find the length of a leg of a 45°-45°-90° triangle with a hypotenuse of length 22. 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. GEOMETRY LESSON 8-2 Use the 45°-45°-90° Triangle Theorem to find the leg. Quick Check 8-3

  6. Special Right Triangles 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? 96= 2 • leg hypotenuse = 2 • leg 96 2 leg = Divide each side by 2. GEOMETRY LESSON 8-2 The distance from one corner to the opposite corner, 96 ft, is the length of the hypotenuse of a 45°-45°-90° triangle. leg = 67.882251 Use a calculator. Each side of the playground is about 68 ft. Quick Check 8-3

  7. Special Right Triangles 18= 3 • shorter leg longer leg = 3 • shorter leg d = Divide each side by 3. d = • Simplify by rationalizing the denominator. d = 18 3 3 d = 6 3 Simplify. f = 2 • 6 3hypotenuse = 2 • shorter leg 18 3 18 3 3 3 f = 12 3 Simplify. The length of the shorter leg is 6 3, and the length of the hypotenuse is 12 3. GEOMETRY LESSON 8-2 Quick Check 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. 8-3

  8. Special Right Triangles GEOMETRY LESSON 8-2 A garden shaped like a rhombus has a perimeter of 100 ft and a 60° angle. Find the area of the garden to the nearest square foot. Because a rhombus has four sides of equal length, each side is 25 ft. Because a rhombus is also a parallelogram, you can use the area formula A = bh. Draw the rhombus with altitude h, and then solve for h. 8-3

  9. Special Right Triangles 25 2 shorter leg = = 12.5 Divide each side by 2. h = 12.5 3 longer leg = 3 • shorter leg A = (25)(12.5 3) Substitute 25 for b and 12.5 3 for h. GEOMETRY LESSON 8-2 (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. Then apply the area formula. 25 = 2 • shorter leg hypotenuse = 2 • shorter leg A = bhUse the formula for the area of a parallelogram. A = 541.26588 Use a calculator. To the nearest square foot, the area is 541 ft2. Quick Check 8-3

  10. Special Right Triangles 12 3, or about 20.8 mm 2 2 , or about 2.8 cm AC = 18; AB = 18 2 AC = 18 3; AB = 36 AC = 6 3; AB = 12 3 GEOMETRY LESSON 8-2 Use ABC for Exercises 1–3. 1. If m A = 45, find AC and AB. 2. If m A = 30, find AC and AB. 3. If m A = 60, find AC and AB. 4. Find the side length of a 45°-45°-90° triangle with a 4-cm hypotenuse. 5. Two 12-mm sides of a triangle form a 120° angle. Find the length of the third side. 8-3

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