Elements

Name __________________________ Date _______________

9.4 Problem Solving Using the Pythagorean Theorem

DO NOWSolve for m1. m2 = 121 2. m2 = 225

3. m2 = 1.96

Evaluate4. 32+ 82 5. 172+ 62 6. 232+ 422

Objective: TSW use properties of triangles to solve real-world problems. TSW use the Pythagorean Theorem to measure indirectly.

You know four properties of triangles:Perimeter__________________________________________________________________________________________________________

Area______________________________________________________________________________________________________________

Similar Triangles_____________________________________________________________________________________________________Pythagorean Theorem __________________________________________________________________________________________________________________________________________________________

Now let’s look at some examples….

EXAMPLE 1aUsing Indirect Measurement

Air Travel A pilot flies 150 miles due south of an airport. He then changes his course and flies 325 miles due east. How far is the pilot from the airport?

Guided PracticeUse the information in the map.

1. A pilot flies 200 miles due north of an airport. He then changes his course and flies 450 miles due west. How far is the pilot from the airport?

EXAMPLE 2aFinding Perimeter and Area

Find the perimeter and area of the triangle.

Find the height of the triangle.

Use the height to find the perimeter and areaGuided PracticeComplete the exercise.

2. Find the perimeter and area of the triangle.

EXAMPLE 3aIdentifying a Pythagorean Triple

Determine whether the side lengths of the triangle form a Pythagorean triple.

a2 + b2 = c2

Definition of Pythagorean triple ____________________________________________________________________________________________________________

Practice for you:Let a and b represent the lengths of the legs of a right triangle, and let c represent the length of the hypotenuse. Find the unknown length. Then find the area and perimeter. Round to the nearest tenth, if necessary.

1. a = 48 ft, b = 55 ft, c = ____

2. a = 26 mm, b = ____, c = 37 mm

3. a = ____, b = 48 in., c = 58 in.

4. a = 4.0 yd, b = 9.6 yd, c = ____

5. a = 78 ft, b = 88 ft, c = ____

6. a = 0.9 mm, b = ____, c = 2.8 mm

Determine whether the numbers form a Pythagorean triple.7. 13, 15, 17

8. 24, 70, 74

9. 24, 45, 51

10. 40, 41, 58

11. A boat in the ocean is 120 miles directly north of a small island. The boat begins to head to shore but is pushed by a wind heading directly east. The boat ends up 50 miles directly east of the island. If the boat traveled in a straight line, how many miles did it travel?

Find the perimeter of the right triangle given its area and the length of one leg. Round to the nearest tenth, if necessary.

12. a = 18 mArea = 63 m2

13. a = 9.4 ftArea = 70.5 ft2

14. a = 12.46 in.Area = 115.255 in.2

Find the value of x.15.

16.

16. Find the value of x.

17. If you double the base and height of a triangle, what happens to the area of the triangle? Explain your reasoning.

In Exercises 1–3, find the perimeter and area of the figure.

4. You are mounting an 8 foot TV antenna on your flat garage roof. The installation kit provides three cables each 10 feet in length that attach to the top of the antenna. How far should each of these cables be placed from the base of the antenna so that the antenna remains vertical?

5. A plane flies in a straight line to Jacksonville. It is 100 miles east and 150 miles north of the point of departure, Osceola. How far did the plane fly?

6. In a football game, a quarterback throws a pass from the 15-yard line, 10 yards from the sideline. The pass is caught on the 40-yard line, 45 yards from the same sideline. How long was the pass?

7. On a softball diamond, the bases are 60 feet apart and meet to form right angles. A base runner is standing on first when the batter hits a long fly ball down the right field line. The base runner takes off for second, rounds second, sprints for third, and slides headfirst into third. What a slide! However, it was a foul ball. So the runner gets up, and jogs straight across the infield back to first. How far did the runner run on this play?

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