Right Triangle Review hypotenuse leg right angle leg

Right Triangle Review hypotenuse leg right angle leg It is a triangle which has an angle that is 90 degrees. The two sides that make up the right angle are called legs. The side opposite the right angle is the hypotenuse.

The Pythagorean Theorem In a right triangle, if a and b are the measures of the legs and c is the hypotenuse, then a 2 + b 2 = c 2. Note: The hypotenuse, c, is always the longest side.

Find the length of the hypotenuse if 1. a = 12 and b = 16. 122 + 162 = c 2 144 + 256 = c 2 400 = c 2 Take the square root of both sides. 20 = c

Find the length of the hypotenuse if 2. a = 5 and b = 7. 52 + 72 = c 2 25 + 49 = c 2 74 = c 2 Take the square root of both sides. 8. 60 = c

Let's find the distance between two points. 8 7 units apart 7 (-6, 4) 6 5 4 3 2 1 (1, 4) So the distance from ( -6, 4) to (1, 4) is 7. -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 -2 -3 -4 -5 -6 -7 If the points are located horizontally from each other, the y coordinates will be the same. You can look to see how far apart the x coordinates are.

What coordinate will be the same if the points are located vertically from each other? (-6, 4) 7 units apart 8 7 6 5 4 3 2 1 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 -2 -3 -4 -5 -6 -7 (-6, -3) So the distance from ( -6, 4) to (-6, -3) is 7. If the points are located vertically from each other, the x coordinates will be the same. You can look to see how far apart the y coordinates are.

But what are we going to do if the points are not located either horizontally or vertically to find the distance between them? Let's start by finding the distance from (0, 0) to (4, 3) 8 7 6 5 4 3 2 1 5? 3 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 -2 -3 -4 -5 -6 -7 4 The Pythagorean Theorem will help us find the hypotenuse So the distance between (0, 0) and (4, 3) is 5 units. This triangle measures 4 units by 3 Let's add some lines and units on the sides. If we find the hypotenuse, we'll have the distance make a right triangle. from (0, 0) to (4, 3)

Now let's generalize this method to come up with a formula so we don't have to make a graph and triangle every time. 8 7 6 2 5 4 3 2 11 Let's start by finding the distance from (x 1, y 1) to (x 2, y ) ? (x 2, y 2) (x , y 1) y 2 – y 1 x -x -7 -6 -5 -4 -3 -2 -1 0 1 2 32 4 5 16 7 8 -2 -3 -4 -5 -6 -7 Again the Pythagorean Theorem will help us find the hypotenuse Solving for c gives us: Let's add some lines and make a right triangle. This is called the distance formula

Let's use it to find the distance between (3, -5) and (-1, 4) Plug these values in the distance formula -1 CAUTION! (x 1, y 1) 3 4 -5 (x 2, y 2) means approximately equal to found with a calculator Don't forget the order of operations! You must do the brackets first then powers (square the numbers) and then add together BEFORE you can square root