8B Pythagorean Theorem: a2 + b2 = c2
(leg #1)2 + (leg #2)2 = (hypotenuse)2
a = leg #1 (adjacent to right angle)
b = leg #2 (adjacent to right angle)
c = hypotenuse (OPPOSITE right Angle)
Hypotenuse always longest side!!
Find the length of the missing side.
Hint: Square Roots undo Squares
1. a = 12, b = 25, c = ? 2. a = 18, b = ?, c = 35 3. a = ?, b = 13, c = 24
Find the value of x.
4. 5. 6.
7. 8.
Determine whether the given lengths are sides of a right triangle. You must show work for credit!
9. 66, 60, 24 10. 16, 34, 30 11. 20, 21, 29 12. 5, 13, 12
Solve the word problems using the Pythagorean Theorem.
· Hint: Draw a picture and label what you know to set up Pythagorean theorem.
13. A ladder 25-ft long is placed so that its top reaches 24 ft up the side of the house. How far from the house is the bottom of the ladder?
14. A tower casts a shadow 40 m long. The distance from the top of the tower to the end of the shadow is 50 m. How high is the tower?
15. Marie and Kevin hiked 3 miles east and then 6 miles north. How far were they from their starting point?
16. A doorway is 1.5 meters wide by 3 meters high. Michael has a 4 meters long square table that he recently found on sale at the store. He wants to know if he bought the table will fit through the doorway to put in the dining room.
17. In a right triangle, the shorter leg is 5 and the hypotenuse is one unit more than the longer leg. Find the length of the hypotenuse.
18. The foot of a ladder is 10 feet from a wall. The ladder is 2 feet longer than the height it reaches on the wall. What is the length of the ladder?
19. In a right triangle, the shorter leg is 7 units less than the longer leg. The hypotenuse is 1 unit more than the longer leg. Find the length of the shorter leg.
20. The hypotenuse of a right triangle is 1 more than twice the length of the shorter leg. The longer leg is 15. Find the hypotenuse.