In a right triangle there are 2 legs and a hypotenuse.
The point where the two legs meet is a right angle
The side across from the right angle is the longest side and it is called the hypotenuse.
4 Pythagorean Theorem a2 b2 c2
The legs are a and b the hypotenuse is c.
c a b The formula says that if you square the legs and add them together you will get the length of the hypotenuse squared. 5 Try this
32 42 x2 9 16 x2 25 x2 5 in. x and -5 in. x (x 5 is the answer that will work in this problem) 52 112 x2 25 121 x2 146 x2 12.08 mi x and -12.08 mi x (x 12.08 is the answer that will work in this problem) x mi. 5 mi. 11 mi. 6 What if we needed the measure of one of the legs
13 ft. x 12 ft. a2 b2 c2 x2 122 132 x2 144 169 x2 25 x 5 ft. a2 b2 c2 x2 42 152 x2 16 225 x2 209 x 14.46 mi. 7 Pythagorean Inequalities
when c is the longest side of a triangle you can tell if the triangle is acute obtuse or right by using the following
acute c2 lt a2 b2
obtuse c2 gt a2 b2
right c2 a2 b2
8 Try this
Determine whether the triangle is right acute or obtuse.
32 62 72
9 36 49
since the hypotenuse is larger than the square of the legs it is an obtuse triangle.
1. 7 3 6
lt 2. 14 52 49 142 492 522 196 2401 2704 2597 lt 2704 Obtuse Triangle 9 Just for fun 10
What is the length of a diagonal of a square with side lengths of 10 units
Step 1 draw it.
Step 2 label it.
Step 3 set up an equation
Step 4 does my answer make sense
x 10 10 10 102 102 x2 100 100 x2 200 x2 14.14 x 10 Try this
What is the length of a diagonal of a square whose side lengths are 5
1. draw it 2. label it 3. set up an equation 4. solve 5. does the answer make sense 52 52 x2 25 25 x2 50 x2 7.07 x 11 Assignment
Practice 5.4 (dont do 16)
Practice 12.3 (all)
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