The Pythagorean Theorem a2 + b2 = c2

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Presentation transcript:

The Pythagorean Theorem a2 + b2 = c2 a2 = c2 – b2 a b c Which side is the hypotenuse? The right angle points to the hypotenuse. It’s the side labelled “c”.

When calculating the hypotenuse, we add the area of the squares of the other two sides. Calculate side c. c2 = a2 + b2 c2 = 82 + 62 6 8 c c2 = 64 + 36 c2 = 100 c = 10

Calculate the length of side x. b2 = c2 – a2 x2 = 122 – 72 a b x 12 7 x2 = 144 – 49 x2 = 95 c When calculating a side, we determine the difference of the area of the square of the hypotenuse and the area of the square of the known side. x = 9.7

The length and width of a rectangle are 12 cm and 15 cm The length and width of a rectangle are 12 cm and 15 cm. Calculate the length of the diagonal. c2 = a2 + b2 d 2 = 152 + 122 d 15 cm 12 cm d 2 = 225 + 144 d 2 = 369 d = 19.2 cm

Tanya is making a party hat using a cone made out of paper Tanya is making a party hat using a cone made out of paper. Determine the height of the cone. b2 = c2– a2 h2 = 132– 52 h2 = 169– 25 h 5 cm 13 cm h2 = 144 h = 12 cm