Bell Work 1/251) 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

95

y

5√3

x

Review 5.7 & 5.81/25

5.7: Pythagorean TheoremWhat is the Pythagorean Theorem?

a2 + b2 = c2

Simplifying radicalsPythagorean tripleClassifying triangles

Right, obtuse and acuteRight: c2 = a2+b2

Obtuse: c2 > a2+b2

Acute: c2 < a2+b2

Example 1: TogetherFind the value of x. Give your answer in simplest radical form.

a2 + b2 = c2 Pyth. Thm.x6

362 + 32 = x2 Substitution

45 = x2

Simplifyx = 3√5 Find the positive

square root & simplify

Example 2: TogetherFind the missing side length. Tell if the sides form a Pythagorean triple. Explain

21.6

a2 + b2 = c2 Pyth. Thm.a2 + (1.6)2 = 22 Substitutiona2 = 1.44 Solve for a2

a = 1.2 Find the positive square root.The side lengths do not form a Pythagorean triple because 1.2 and 1.6 are not whole numbers

Exercises: On Your Own!!Find the value of x. Give your answer in simplest radical form

x

6

1) 2 2) 14

x8

Find the missing side length. Tell if the sides form a Pyth. triple. 3)

x

24

32Tell if the measures can be the side length of a triangle. If so, is it right, acute, or obtuse

4) 5)6) 7)

9, 12, 16

1.5, 3.6, 3.9

11, 14, 27

2, 3.7, 4.1

5-8: Applying Special Right Triangle

45°-45°-90° Theorem

30°-60°-90° Theorem

Examples: Together

x

x

45°

45°19

15

x45° 45°

22

yx

60° 30°

Find the values of the variables. Give your answers in simplest radical form.1)

2)

3)

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

Divide both sides √2 15 = x √2 15√2 = x √2

Rationalize the denominator

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

Exercises: On Your Own!Find the values of the variables. Give your answers in simplest radical form.

x

2645°

1) 2)

4)

3)

x12

x

x16√2

45°

45°

x 48

y

30°

60° 5)

x

y

6 30°