Vocab.
What is the name of the formula a2+b2=c2
Pythagorean Theorem
Use the Pythagorean theorem to find c.
A=3, B=4
5
Is it a right triangle?
1-2-3
No
A2 + B2 ≠ C2
Find the distance between the points (1,2) and (4,6)
5 units
The bottom of a ladder must be placed 3 feet from a wall. The ladder is 12 feet long. How far above the ground does the ladder touch the wall?
11.62 feet
What type of triangles is Pythagorean Theorem used for?
Right Triangles
Find the missing leg for the triangle with a= 8 and c=17.
b = 15
Is it a right triangle?
30-40-50
Yes!
A2 + B2 = C2
Find the distance between the points (-3,-2) and (3,6)
10 units
Two runners jog 8 miles north and then 5 miles west. What is the shortest diagonal distance back to their starting point?
9.43 miles
In the Pythagorean theorem, what are "a" and "b" called?
Legs
Find the missing hypotenuse for the triangle whose legs are 5 and 12.
13
Is it a right triangle?
10-11-21
No
A2 + B2 ≠ C2
A submarine is traveling underwater at coordinates (-2,-5). A sunken ship is located at coordinates (-9,-10). Each unit represents 1 kilometer.
What is the shortest distance between the submarine and the sunken ship in kilometers? Round to the nearest hundredth.
8.6 kilometers
How far from the base of a house do you need to place a 15' ladder so that it exactly reaches the top of a 12' wall?
9 feet
In the Pythagorean Theorem, what is "c" called?
Hypotenuse
Find the missing leg for the triangle with 29 and 20.
a = 21
Is it a right triangle?
9-40-41
Yes!
A2 + B2 = C2
A rescue team is tracking a lost hiker. The hiker's last known location is (-5,-2), and the rescue team's location is (7,7). Each unit represents one mile. How far apart are the hiker and rescue team in a straight line? Round to the nearest hundredth.
15 miles
A park ranger is planning a triangular walking path through a park. The path will have three straight sections measuring 8 meters, 11 meters, and 14 meters. The ranger wants the two shorter sections to meet at a perfect 90° angle.
Will the walking path form a right triangle?
No. 185 = 196
We know that three numbers represent a right triangle by using the _________ of the Pythagorean Theorem.
Converse
Find the missing leg for the triangle with 12 and 37.
a = 35
Is it a right triangle?
54-72-90
Yes!
A2 + B2 = C2
A boat leaves a marina and travels 6 miles west and 8 miles north. Another boat leaves the same marina and travels 2 miles east and 4 miles south. To the nearest hundredth, how many miles apart are the two boats?
14.42 miles
A rectangular park is 25 meters long diagonally from one corner to the opposite corner. The park is 7 meters wide. What is the length of the park?
24 meters