bell ringer. 30-60-90 triangles a right triangle with angle measures of 30, 60, and 90 are called...

Download Bell Ringer. 30-60-90 Triangles A Right Triangle with angle measures of 30, 60, and 90 are called 30-60-90 triangles

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Bell Ringer Slide 2 30-60-90 Triangles A Right Triangle with angle measures of 30, 60, and 90 are called 30-60-90 triangles. Slide 3 Example 1 Find Leg Length SOLUTION You can use the Pythagorean Theorem to find the value of b. (leg) 2 + (leg) 2 = (hypotenuse) 2 Write the Pythagorean Theorem. 1 2 + b 2 = 2 2 Substitute. 1 + b 2 = 4 Simplify. b 2 = 3 Subtract 1 from each side.Take the square root of each side. b =3 In the diagram, PQR is a 30 60 90 triangle with PQ = 2 and PR = 1. Find the value of b. Slide 4 Example 2 Find Hypotenuse Length SOLUTION The hypotenuse of a 30 60 90 triangle is twice as long as the shorter leg. hypotenuse = 2 shorter leg 30 60 90 Triangle Theorem = 2 12 Substitute. = 24 Simplify. In the 30 60 90 triangle at the right, the length of the shorter leg is given. Find the length of the hypotenuse. ANSWER The length of the hypotenuse is 24. Slide 5 Example 3 Find Longer Leg Length In the 30 60 90 triangle at the right, the length of the shorter leg is given. Find the length of the longer leg. ANSWER The length of the longer leg is 5. 3 30 60 90 Triangle Theorem longer leg = shorter leg 3 Substitute. = 5 3 SOLUTION The length of the longer leg of a 30 60 90 triangle is the length of the shorter leg times. 3 Slide 6 Now You Try Find Lengths in a Triangle ANSWER 14 Find the value of x. Write your answer in radical form. 1. 2. 3. ANSWER 3 3 103 Slide 7 Example 4 Find Shorter Leg Length In the 30 60 90 triangle at the right, the length of the longer leg is given. Find the length x of the shorter leg. Round your answer to the nearest tenth. 2.9 x Use a calculator. ANSWER The length of the shorter leg is about 2.9. Substitute. 5 = x 3 30 60 90 Triangle Theorem longer leg = shorter leg 3 SOLUTION The length of the longer leg of a 30 60 90 triangle is the length of the shorter leg times 3. = x 5 3 Divide each side by. 3 Slide 8 Example 5 Find Leg Lengths In the 30 60 90 triangle at the right, the length of the hypotenuse is given. Find the length x of the shorter leg and the length y of the longer leg. SOLUTION Use the 30 60 90 Triangle Theorem to find the length of the shorter leg. Then use that value to find the length of the longer leg. Shorter leg hypotenuse = 2 shorter leg Longer leg longer leg = shorter leg 3 8 = 2 xy = 4 3 4 = xy = 43 Slide 9 Example 5 Find Leg Lengths ANSWER The length of the shorter leg is 4. The length of the longer leg is 4. 3 Slide 10 Now You Find Leg Lengths ANSWER 3.5 Find the value of each variable. Round your answer to the nearest tenth. 4. 5. ANSWER x = 21 ; y = 21 36.4 3 Slide 11 Page 552 Slide 12 Page 552 #s 2-36 even only

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