1. Bell Work 1/25
1) Find the value of x. Give the answer in simplest radical form
2) Find the values of the variables. Give your answers in simplest radical form. x 9 5 y
5√3 x

2. Review 5.7 & 5.8
1/25

3. 5.7: Pythagorean Theorem What is the Pythagorean Theorem?
a2 + b2 = c2
Simplifying radicals
Pythagorean triple
Classifying triangles
Right, obtuse and acute
Right: c2 = a2+b2
Obtuse: c2 > a2+b2
Acute: c2 < a2+b2

4. Example 1: Together x 6 a2 + b2 = c2 Pyth. Thm.
Find the value of x. Give your answer in simplest radical form.
a2 + b2 = c2 Pyth. Thm.
= x2 Substitution 3
45 = x Simplify
x = 3√5 Find the positive square root & simplify

5. Example 2: Together 2 1.6 a2 + b2 = c2 Pyth. Thm.
Find the missing side length. Tell if the sides form a Pythagorean triple. Explain
a2 + b2 = c2 Pyth. Thm.
a2 + (1.6)2 = 22 Substitution
a2 = Solve for a2
a = Find the positive square root.
The side lengths do not form a Pythagorean triple because 1.2 and 1.6 are not whole numbers

6. Exercises: On Your Own!! 14 x 1) 2) x 6 2 8 x 24 3) 32 4) 5) 6) 7)
Find the value of x. Give your answer in simplest radical form 1) 2) x 6 2 8 x 24
Find the missing side length. Tell if the sides form a Pyth. triple. 3) 32
Tell if the measures can be the side length of a triangle. If so, is it right, acute, or obtuse 4)
9, 12, 16 5)
11, 14, 27 6) 7)
1.5, 3.6, 3.9
2, 3.7, 4.1

7. 5-8: Applying Special Right Triangle
45°-45°-90° Theorem
30°-60°-90° Theorem

8. Examples: Together x 15 x y x 22 1) 2) 3)
Find the values of the variables. Give your answers in simplest radical form. 1) x
45° 19
This is a 45°-45°-45° triangle.
x = 19√2 Hyp.=leg√2
This is a 45°-45°-45° triangle.
15 = x√2 Hyp.=leg√2 15 x
45° 2)
15 = x √2
Divide both sides √2
Rationalize the denominator
15√2 = x √2
This is a 30°-60°-90° triangle.
22 = 2x Hyp.=2(shorter leg)
11 = x Divide both sides by 2
Y = 11√3 Longer leg = (shorter leg √3 3) 22 y x
60°
30°

9. Exercises: On Your Own! 26 12 x x x x y y x 6 48 x
Find the values of the variables. Give your answers in simplest radical form. x 12 x
16√2
45° 3) 1) x 26
45° 2) x
45° x 48 y 4) x y 5)
60°
30° 6
30°