# 8-3 Special Right Triangles

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8-3 Special Right Triangles

Special Right Triangles
May 9, 2003 Special Right Triangles GEOMETRY LESSON 8-2 (For help, go to Lesson 1-6.) 3. Use a protractor to find the measures of the angles of each triangle. Check Skills You’ll Need 8-3

Special Right Triangles
May 9, 2003 Special Right Triangles GEOMETRY LESSON 8-2 Solutions 1. 45, 45, , 60, 90 3. 45, 45, 90 8-3

Special Right Triangles
May 9, 2003 Special Right Triangles GEOMETRY LESSON 8-2 Find the length of the hypotenuse of a 45°-45°-90° triangle with legs of length Use the 45°-45°-90° Triangle Theorem to find the hypotenuse. h = • hypotenuse = 2 • leg h = Simplify. h = (3) h = 5(2) 3 h = The length of the hypotenuse is Quick Check 8-3

Special Right Triangles
May 9, 2003 Special Right Triangles GEOMETRY LESSON 8-2 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. 22 = 2 • leg hypotenuse = • leg 22 2 x = Divide each side by 22 2 x = • Simplify by rationalizing the denominator. 2 x = x = Simplify. The length of the leg is Quick Check 8-3

Special Right Triangles
May 9, 2003 Special Right Triangles GEOMETRY LESSON 8-2 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. 96 = • leg hypotenuse = • leg leg = Divide each side by 2. 96 2 leg = Use a calculator. Each side of the playground is about 68 ft. Quick Check 8-3

Special Right Triangles
May 9, 2003 Special Right Triangles 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. 18 = 3 • shorter leg longer leg = • shorter leg d = Divide each side by 3. 18 3 d = • Simplify by rationalizing the denominator. 3 18 3 d = d = Simplify. f = 2 • hypotenuse = 2 • shorter leg f = Simplify. The length of the shorter leg is , and the length of the hypotenuse is 8-3

Special Right Triangles
May 9, 2003 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

Special Right Triangles
May 9, 2003 Special Right Triangles 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 shorter leg = = Divide each side by 2. 25 2 h = longer leg = 3 • shorter leg A = bh Use the formula for the area of a parallelogram. A = (25)( ) Substitute 25 for b and for h. A = Use a calculator. To the nearest square foot, the area is 541 ft2. Quick Check 8-3

Special Right Triangles
May 9, 2003 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. AC = 18; AB = AC = ; AB = 36 AC = ; AB = , or about 2.8 cm , or about 20.8 mm 8-3