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Example 3-2b Objective Find missing measures in degree right triangles and degree triangles

Example 3-2b Review Vocabulary Pythagorean Theorem In a right triangle, the square of the length of the hypotenuse c is equal to the sum of the squares of the length of the legs a and b. C 2 = A 2 + B 2

Example 3-2b 30 0 – 60 0 Triangle A = ½ of C or 2A = C Remember: A is the shortest leg using the Pythagorean Theorem C 2 = A 2 + B 2 A B C

Example 3-2b 45 0 – 45 0 Triangle A and B are congruent A B C

Lesson 3 Contents Example 1Find Lengths of a 30  –60  Right Triangle Example 2Find the Lengths of a 45  Example 2Find the Lengths of a 45  –45  Right Triangle45  Right Triangle

Example 3-1a Find each missing length. Round to the nearest hundredth if necessary. 1/2 Remember: A triangle, the hypotenuse is twice the side opposite the 30 0 angle C = 2(6) Multiply C = 12 c = 12 in Since it is a right triangle and 2 of the 3 sides are known, use the Pythagorean Theorem c 2 = a 2 + b 2

Example 3-1a Find each missing length. Round to the nearest hundredth if necessary. 1/2 Replace c with 12 C = 2(6) C = 12 c = 12 in c 2 = a 2 + b Replace a with = = b 2 Bring down + b Follow Order of Operations P E MD AS Do all exponents first

Example 3-1a Find each missing length. Round to the nearest hundredth if necessary. 1/2 C = 12 c = 12 in c 2 = a 2 + b = b 2 Follow Order of Operations P E MD AS Do all exponents first = 36 Bring down + b = 36 + b 2 Ask “What is being done to b 2 ? b 2 is being added by 36 Do the inverse on both sides of the equal sign

Example 3-1a Find each missing length. Round to the nearest hundredth if necessary. 1/2 C = 12 c = 12 in c 2 = a 2 + b = b 2 Bring down = = 36 + b Subtract Bring down = = 36 Subtract = Bring down + b = b 2 Combine “like” terms = 0 Bring down + b = 0 + b 2

Example 3-1a Find each missing length. Round to the nearest hundredth if necessary. 1/2 C = 12 c = 12 in c 2 = a 2 + b = b 2 Use the Identity Property to add 0 + b = = 36 + b = b = 0108 = 0 + b = b 2 Ask “what is being done to the variable?” The variable is being squared Do the inverse on both sides of the equal sign

Example 3-1a Find each missing length. Round to the nearest hundredth if necessary. 1/2 C = 12 c = 12 in Find the square root of = b 2 Find the square root of b 2 Combine “like” terms = b Remember: Had to solve for c and for b so need both answers with dimensional analysis Answer: b = inches c = 12 inches

Example 3-1b Find each missing length. Round to the nearest hundredth if necessary. Answer: a = 10 cm, b = cm 1/2

Example 3-2a BASEBALL The figure below shows the dimensions of a baseball diamond. The distance between home plate and first base is 90 feet. The area between first base, third base, and home plate forms a right triangle. Find the distance from first base to third base and the distance from third base to home plate. 2/2 Remember: A degree triangle has congruent legs Find the right triangle area between first base, third base, and home plate forms aright triangle Since it is a right triangle, can use the Pythagorean Theorem 90 ft

Example 3-2a 2/2 Write the Pythagorean Theorem c 2 = a 2 + b 2 Define the variable c as the hypothesis since it is unknown cc2c2 Replace a and b with 90 since they are congruent c 2 = ft

Example 3-2a 2/2 Bring down c 2 c 2 = a 2 + b 2 c2c2 c 2 = c 2 = Combine “like” terms c 2 = 8,100c 2 = 8, ,100 Combine “like” terms again c 2 = 16,200 Ask “what is being done to the variable?” The variable is being squared Do the inverse on both sides of the equal sign Find the square root of c 2 c Find the square root of 16,200 c =

Example 3-2a 2/2 c 2 = a 2 + b 2 c2c2 c 2 = c 2 = Add dimensional analysis c 2 = 8,100c 2 = 8, ,100 c 2 = 16,200 c c = c = ft Answer: Remember: Had to solve for 2 dimensions Third to Home = 90 ft First to 3 rd = ft Find the distance from first base to third base and the distance from third base to home plate.

Example 3-2b SAILING The sail of a sailboat is in the shape of a right triangle. The height of the sail is 12 feet. Find each missing length. Answer: b = 12 ft; c = ft * 2/2

End of Lesson 3 Assignment Lesson 6:3Special Right Triangles All