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Example 3A: Finding Side Lengths in a 30º-60º-90º Triangle

A 30°-60°-90° triangle is another special right triangle. You can use an equilateral triangle to find a relationship between its side lengths. Example 3A: Finding Side Lengths in a 30º-60º-90º Triangle. Find the values of x and y . Give your answers in simplest radical form. 22 = 2 x.

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Example 3A: Finding Side Lengths in a 30º-60º-90º Triangle

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  1. A 30°-60°-90° triangle is another special right triangle. You can use an equilateral triangle to find a relationship between its side lengths.

  2. Example 3A: Finding Side Lengths in a 30º-60º-90º Triangle Find the values of x and y. Give your answers in simplest radical form. 22 = 2x Hypotenuse = 2(shorter leg) 11 = x Divide both sides by 2. Substitute 11 for x.

  3. Example 3B: Finding Side Lengths in a 30º-60º-90º Triangle Find the values of x and y. Give your answers in simplest radical form. Rationalize the denominator. y = 2x Hypotenuse = 2(shorter leg). Simplify.

  4. Substitute for x. Check It Out! Example 3a Find the values of x and y. Give your answers in simplest radical form. Hypotenuse = 2(shorter leg) Divide both sides by 2. y = 27

  5. Check It Out! Example 3b Find the values of x and y. Give your answers in simplest radical form. y = 2(5) y = 10 Simplify.

  6. Check It Out! Example 3c Find the values of x and y. Give your answers in simplest radical form. 24 = 2x Hypotenuse = 2(shorter leg) 12 = x Divide both sides by 2. Substitute 12 for x.

  7. Check It Out! Example 3d Find the values of x and y. Give your answers in simplest radical form. Rationalize the denominator. Hypotenuse = 2(shorter leg) x = 2y Simplify.

  8. Example 4: Using the 30º-60º-90º Triangle Theorem An ornamental pin is in the shape of an equilateral triangle. The length of each side is 6 centimeters. Josh will attach the fastener to the back along AB. Will the fastener fit if it is 4 centimeters long? Step 1 The equilateral triangle is divided into two 30°-60°-90° triangles. The height of the triangle is the length of the longer leg.

  9. Example 4 Continued Step 2 Find the length x of the shorter leg. 6 = 2x Hypotenuse = 2(shorter leg) 3 = x Divide both sides by 2. Step 3 Find the length h of the longer leg. The pin is approximately 5.2 centimeters high. So the fastener will fit.

  10. Check It Out! Example 4 What if…? A manufacturer wants to make a larger clock with a height of 30 centimeters. What is the length of each side of the frame? Round to the nearest tenth. Step 1 The equilateral triangle is divided into two 30º-60º-90º triangles. The height of the triangle is the length of the longer leg.

  11. Check It Out! Example 4 Continued Step 2 Find the length x of the shorter leg. Rationalize the denominator. Step 3 Find the length y of the longer leg. y = 2x Hypotenuse = 2(shorter leg) Simplify. Each side is approximately 34.6 cm.

  12. Lesson Quiz: Part I Find the values of the variables. Give your answers in simplest radical form. 1.2. 3.4. x = 10; y = 20

  13. Lesson Quiz: Part II Find the perimeter and area of each figure. Give your answers in simplest radical form. 5. a square with diagonal length 20 cm 6. an equilateral triangle with height 24 in.

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