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EXAMPLE 1

The infield of a softball field is a square with a side length of 60 feet. A catcher throws the ball from home plate to second base. How far does the catcher have to throw the ball?. EXAMPLE 1. Using a 45 o –45 o –90 o Triangle. Softball. SOLUTION.

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EXAMPLE 1

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  1. The infield of a softball field is a square with a side length of 60 feet. A catcher throws the ball from home plate to second base. How far does the catcher have to throw the ball? EXAMPLE 1 Using a 45o–45o–90o Triangle Softball SOLUTION To find the distance, use the rule for a 45o–45o–90o triangle.

  2. =leg 2 2 = 60 60(1.414) ANSWER A catcher has to throw the ball about 85 feet. EXAMPLE 1 Using a 45o–45o–90o Triangle hypotenuse = 84.84

  3. ANSWER The distance diagonally across the park is about 212ft for Example 1 GUIDED PRACTICE City Parks 1. A city park is shaped like a square with a side length of 150 feet. What is the distance diagonally across the park?

  4. Find the value of each variable in the triangle. Give the exact answer. hypotenuse = shorter leg 2 x 2 = 10 x 5 = EXAMPLE 2 Using a 30o–60o–90o Triangle You need to find the length of the shorter leg first in order to find the length of the longer leg. STEP 1 Find the length of the shorter leg. Rule for 30o–60o–90o triangle Substitute. Divide each side by 2.

  5. longer leg = shorter leg 3 y 3 = 5 ANSWER 3 The shorter leg is 5 units long. The longer leg is 5 units long. EXAMPLE 2 Using a 30o–60o–90 Triangle STEP 2 Find the length of the longer leg. Rule for 30o–60o–90o triangle Substitute.

  6. 2. ANSWER The value for x =25 in.y = in. 25 3 for Example 2 GUIDED PRACTICE Find the value of each variable. Give the exact answer.

  7. ANSWER The value for x = 7m, y = 14m 3. for Example 2 GUIDED PRACTICE

  8. 4. ANSWER The value forx = 2cm andy = 2 cm 3 for Example 2 GUIDED PRACTICE

  9. Water Ski Show hypotenuse = shorter leg 2 x 2 = 26 x 13 = EXAMPLE 3 Rotating 180 The pyramid ski show is a common attraction at water parks. Find the horizontal distance from the pyramid to the boat. STEP 1 Find the length of the shorter leg.

  10. longer leg = shorter leg 3 y 3 = 13 22.52 ANSWER The horizontal distance is about 23 feet. EXAMPLE 3 Using a Special Right Triangle STEP 2 Find the length of the longer leg.

  11. 3 In Example 3, suppose that the horizontal distance from the pyramid to the boat is 15 feet. What is the distance from the top of the pyramid to the boat? ANSWER The distance from the top of the pyramid to the boat is 30ft. for Example 3 GUIDED PRACTICE 5.What If?

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