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.

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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

Review 5.7 & 5.8 1/25

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

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. 62 + 32 = x2 Substitution 3 45 = x2 Simplify x = 3√5 Find the positive square root & simplify

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 = 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!! 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

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

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°

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°