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Bell Work 1/25

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. y. x. 9. 5√3. 5. x. Review 5.7 & 5.8. 1/25. 5.7: Pythagorean Theorem. What is the Pythagorean Theorem? a 2 + b 2 = c 2

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Bell Work 1/25

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  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. y x 9 5√3 5 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 Find the value of x. Give your answer in simplest radical form. x 6 • a2 + b2 = c2Pyth. Thm. • 62 + 32 = x2 Substitution 3 • 45 = x2 Simplify • x = 3√5 Find the positive square root & simplify

  5. Example 2: Together Find the missing side length. Tell if the sides form a Pythagorean triple. Explain 2 1.6 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

  6. Exercises: On Your Own!! 2) 1) 2 8 Find the value of x. Give your answer in simplest radical form x x 14 24 6 x 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) 5) 9, 12, 16 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 Find the values of the variables. Give your answers in simplest radical form. 1) This is a 45°-45°-45° triangle. x = 19√2 Hyp.=leg√2 15 22 y x x x 45° This is a 45°-45°-45° triangle. 15 = x√2 Hyp.=leg√2 19 45° 45° 45° 15 = x √2 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) x 60° 30°

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

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