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The Pythagorean Theorem

Use the Pythagorean Theorem to find the height of a ladder leaning against a building. Solve for the missing length using the given measurements.

haroldstone
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The Pythagorean Theorem

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  1. The Pythagorean Theorem

  2. A 15 foot ladder leans up against a building. The foot of the ladder is 5 feet from the base of the building. How high up the wall, to the nearest foot does the ladder reach? a2 + b2 = c2 15 a2 + 52 = 152 ? a2 + 25 = 225 5 a2 = 200 ― √ a = 200 a = 14.1

  3. Tim rode 8 miles due north, then 3 miles due east. How far, to the nearest mile, is Tim from where he started? 3 a2 + b2 = c2 82 + 32 = c2 64 + 9 = c2 8 ? 73 = c2 ― √ 73 = c 8.5 = c

  4. Laptop screen sizes are determined by the length of the diagonal portion of the screen, rounded to the nearest whole number. A laptop screen has a 10 inch width and the height measures 8 inches. Calculate the screen size. a2 + b2 = c2 10 82 + 102 = c2 ? 64 + 100 = c2 8 164 = c2 ― √ 164 = c 12.8 = c

  5. A baseball diamond is a square that is 90’ on each side.  If a player throws the ball from 2nd base to home, how  far will the ball travel?  a2 + b2 = c2 902 + 902 = c2 90 8100 + 8100 = c2 ? 16200= c2 ― √ 90 16200 = c 127.3 = c

  6. An isosceles triangle has congruent sides of 20 cm.   The base is 10 cm.  What is the  height of the triangle?  a2 + b2 = c2 52 + b2 = 202 20 20 25 + b2 = 400 ? b2 = 375 5 ― 10 √ b = 375 a = 19.3

  7. You can get around a rectangular park by walking up one side that is 10 feet long and along another side that is 15 feet long. How much distance would you save if you walked across the park instead of around it? Distance Across Distance Around a2 + b2 = c2 10 + 15 =25 102 + 152 = c2 15 ? Distance saved 100 + 225 = c2 325 = c2 ― 25 - 18 = 7 √ 325 = c 10 18 = c

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