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The Pythagorean Theorem. We are learning to…solve for the missing side of right triangles using the Pythagorean Theorem. Friday, August 8, 2014. The Pythagorean Theorem. Right Triangle – a triangle with one right angle Make a drawing of a right triangle.
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The Pythagorean Theorem We are learning to…solve for the missing side of right triangles using the Pythagorean Theorem. Friday, August 8, 2014
The Pythagorean Theorem • Right Triangle – a triangle with one right angle • Make a drawing of a right triangle. • Why can a right triangle not have more than one right angle? • Hypotenuse – the longest side of a right triangle; can always be found across from the right angle on a right triangle. • Label the hypotenuse on your drawing. • Leg of a Right Triangle – the two other sides of the triangle which are not the hypotenuse • Label the legs on your drawing. Hypotenuse Leg Leg
The area of squares built on the legs of a right triangle are equal to the sum of the area of the square built on the hypotenuse. What Pythagoras Discovered: 9 + 16 = 25 25 square units Area of square on a leg + Area of square on a leg = Area of square on a hypotenuse 3 5 5 a 3 c 9 square units b (a)(a) = (c)(c) + (b)(b) 4 a2 + b2 = c2 …this is known as the Pythagorean Theorem 16 square units 4 We can use the Pythagorean Theorem to solve for missing sides of right triangles.
The Pythagorean TheoremExample #1 ? 5 cm 12 cm We are looking for the hypotenuse! a2 + b2 = c2 52 + 122 = c2 25 + 144 = c2 169 = c2 The missing length of the hypotenuse is 13 centimeters long.
The Pythagorean TheoremExample #2 25 ft 24 ft ? We are looking for a leg! a2 + b2 = c2 a2 = 49 a2 + 242 = 252 a2 + 576 = 625 a = 7 a2 + 576 – 576 = 625 – 576 The missing length of the leg is 7 feet.
The Pythagorean TheoremExample #3 15 m 8 m ? We are looking for the hypotenuse! a2 + b2 = c2 82 + 152 = c2 64 + 225 = c2 289 = c2 The missing length of the hypotenuse is 17 meters long.
The Pythagorean TheoremExample #4 20 in 29 in ? We are looking for a leg! a2 + b2 = c2 a2 = 441 a2 + 202 = 292 a2 + 400 = 841 a = 21 a2 + 400 – 400 = 841 – 400 The missing length of the leg is 21 inches.
Find the length of the missing side of the right triangle below: ? • 43 meters • 50 meters • 52 meters • 68 meters • I need help. 48 m 20 m
A rectangular garden has the dimensions shown below. 29 m 20 m • 441 meters • 25 meters • 21 meters • 35.2 meters • I need help. ? Find the missing length of the garden.
In class, Juanita sits directly in front of Harold, 8 feet away, and directly to the left of Ian, 6 feet away.What is the distance, in feet, from Ian to Harold? • 10 feet • 14 feet • 5.29 feet • 100 feet • I need help.