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Section 8.3 Special Right Triangles !

Section 8.3 Special Right Triangles !. L.T.: Be able to find sides of 45-45-90 triangles!. Quick Review: Rationalize the following!. 3. 8. 3. 8. x. x. x. 5. 45 °. 5. y. Find the length of the hypotenuse:. 45-45-90 Triangle Theorem:

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Section 8.3 Special Right Triangles !

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  1. Section 8.3Special Right Triangles! L.T.: Be able to find sides of 45-45-90 triangles! Quick Review: Rationalize the following!

  2. 3 8 3 8 x x x 5 45° 5 y Find the length of the hypotenuse: 45-45-90 Triangle Theorem: In a 45-45-90 triangle, both ______ are congruent (isosceles), and the length of the hypotenuse is _____ times the length of each leg. legs Find the value of each variable:

  3. y x x 45° 45° y x 45°

  4. x 45° y x 45° Find the value of each variable!

  5. 45° 45° Find the area of the triangle!

  6. Why do we need to know about 45-45-90 triangles? They are in the real world! Not to mention, it’s a whole lot easier than using the Pythagorean Theorem. Yadier Molina wants to know how far he has to throw the ball to catch a man stealing second. Before, we had to use the Pythagorean Theorem. But now that you know about 45-45-90 triangles, you can use the shortcut! 90 ft x ft 90 ft

  7. x 45° Final Example Find the value of x.

  8. 5 y x 45° 45° y x Section 8.3 Part 2Special Right Triangles! L.T.: Be able to find sides of 30-60-90 triangles! Quick Review:

  9. 60° hypotenuse “shorty” 30° “longy” Question: In a 30-60-90 triangle, will any sides be the same length? No! • 30-60-90 Triangle Theorem: • In a 30-60-90 triangle, • the length of the hypotenuse is ____ times the length of the shorter leg (shorty) • the length of the longer leg (longy) is _____ times the length of the shorter leg (shorty) 2

  10. 15 y x x 30° 3 x 30° y 30° 5 y 60° 7 x y Find the value of each variable!

  11. 12 15 60° y y x x 30° 30° x x 30° y y 5

  12. Let’s practice some more! 6 60° 30° Find the area of each triangle.

  13. d b 60° c a 45° A window-washer leans a 40-foot ladder against the side of a building. The base of the ladder make a 60° angle with the ground. How high up the side of the building does the ladder reach? 40 ft y 60° x Find the value of each variable.

  14. d a c b 60° 45° Did we meet the target? L.T.: Be able to find sides of 30-60-90 triangles! Find the value of each variable!

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