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Main Idea NGSSS Example 1: Solve a Right TriangleExample 2: Real-World ExampleFive-Minute Check

• Solve problems using the Pythagorean Theorem.

MA.8.G.2.4 Validate and apply Pythagorean Theorem to find distances in real world situations or between points in the coordinate plane.

Solve a Right Triangle

RAMPS A boat ramp has a base that is 25 feet long and 4.2 feet high. Write an equation that can be used to find the length of the ramp. Then solve. Round to the nearest tenth.

a2 + b2 = c2 Pythagorean Theorem

4.22 + 252 = c2 Replace a with 4.2 and b with 25.

Solve a Right Triangle

Answer: Since length cannot be negative, the boat

ramp is about 25.4 feet long.

17.64 + 625 = c2 Evaluate 4.22 and 252.

642.64 = c2 Add 17.64 and 625.

Definition of square root

± 25.4 c Use a calculator.

A. 16 – 7.5 = x; 8.5 feet

B. 162 – 7.52 = x2; 14.1 feet

C. 162 + 7.52 = x2; 17.7 feet

D. 162 + 7.52 = x; 23.5 feet

STAIRS The stairs leading up to a commuter plane has a base that is 16 feet long and 7.5 feet high. Write an equation that can be used to find the length of the stairs. Then solve. Round to the nearest tenth.

CAMPING The cross section of a camping tent is shown below. Find the width of the base of the tent.

Each half of the cross section forms a right triangle. Use the Pythagorean Theorem.

x x

a2 + b2 = c2 Pythagorean Theorem

82 + x2 = 102 Replace a with 4.8 and c with 10.

64 + x2 = 100 Evaluate 82 and 102.

64 – 64 + x2 = 100 – 64 Subtract 64 from each side.

x2 = 36 Simplify.

Definition of square root

x = 6 or –6 Simplify.Answer: The width of the base of the tent is x + x

or 6 + 6 = 12 feet.

A. 52.9 in.

B. 81.9 in.

C. 96.9 in.

D. 105.9 in.

DESIGN The design shown below is formed by two isosceles triangles. What is the perimeter of the design? Round to the nearest tenth if necessary

A. 3002 + 2002 = p2; 360.6 mi

B. 3002 + 2002 = p; 130,000 mi

C. 3002 - 2002 = p2; 223.6 mi

D. 300 + 200 = p; 500 mi

Write an equation that can be used to answer the question. Then solve. Round to the nearest tenth if necessary.The plane is traveling from point A to point B. How far will the plane have flown when it reaches its destination?

A. 4 + 3 = r; 7 ft

B. 42 + 32 = r; 25 ft

C. 42 + 32 = r2; 5 ft

D. 42 - 32 = r2; 2.6 ft

Write an equation that can be used to answer the question. Then solve. Round to the nearest tenth if necessary.A girl is pinning ribbon to a 3-foot by 4-foot bulletin board. How long will the ribbon have to be to stretch from corner to corner diagonally?

A. 42 in.

B. 58 in.

C. 72 in.

D. 84 in.

Triangle ABC is a right triangle. What is the perimeter of the triangle?