advertisement

Ch. 3-2 & 3-3 The Pythagorean Theorem http://vimeo.com/56785102 http://www.youtube.com/watch?v=nbopLhP4kpo Ch. 3-2 & 3-3 The Pythagorean Theorem Hypotenuse a c Leg -The Pythagorean Theorem is an equation that shows the relationship between hypotenuse and legs of right triangles. a2 + b2 = c2 where a and b are the legs and c is the hypotenuse Must be a right triangle Leg b -You use the Pythagorean theorem to find a missing leg or hypotenuse of a right triangle. Example 1: Find the length of the hypotenuse of the right triangles below. a.) b.) Plug into the formula 52 + 122 = c2 5 cm. c 12 cm. 25 + 144 = c2 c = 169 13 cm c 12 24 Plug into the formula 242 + 122 = c2 576 + 144 = c2 c= 720 27 Example 2: Find the length of the missing legs below. a.) b 9 cm 15 cm Formula: c2 - a2 = b2 Round to nearest one Plug into the formula 152 - 92 = b2 225 - 81 = b2 b2 = 144 Take the square root on both sides b = 12 cm Formula: c2 - a2 = b2 Round to nearest tenth Plug into the formula 182 - 52 = a2 324 - 25 = a2 a2 = 299 b.) 18 cm a Take the square root on both sides a = 17.3 cm 5 cm Example 3: Draw each situation below to figure out if you are solving for a leg or a hypotenuse. Then solve the problem a.) A 10 ft. long slide is attached to a deck that is 5 ft. high. Find the distance from the bottom of the deck to the bottom of the slide to the nearest tenth. 8.7 ft. 10 5 ? b.) A ramp is 1 ft. high. The base of the ramp extends 14 ft. along the side of a building. How long is the sloped part of the ramp to the nearest hundredth of a foot.? ?? 1 14.04 ft. ? Pythagorean Theorem used in roofing! Homework • Pg. 114 Pg. 120 2-20 even & 2-18 even • Ec pg 608 5-16all round to nearest whole number.