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SWBAT use the properties of 30-60-90 triangles to find the side lengths of special right triangles

November 9, 2011 SWBAT use the properties of 30-60-90 triangles to find the side lengths of special right triangles.

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SWBAT use the properties of 30-60-90 triangles to find the side lengths of special right triangles

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  1. November 9, 2011SWBAT use the properties of 30-60-90 triangles to find the side lengths of special right triangles

  2. 1. How many inches are in 2,424 feet?2. A plane is flying at 36,000 feet. Given that 1ft≈0.305 meters, how many meters is the plane above ground?3. If I shot 63 free throws and made 47 of them, what percent did I make?4. 5.

  3. SWBAT use the properties of 30-60-90 triangles to find the side lengths of special right triangles • Review of right triangles • Hypotenuse • Side opposite of the right angle • Longest side of the right triangle • Legs • Sides that make up the right angle

  4. 30 – 60 – 90 Triangle 3 sides of a 30-60-90 • Shorter Side • Opposite the 30° angle • We will call this “x” • Longer Side • Opposite the 60° angle • Equals • Hypotenuse • Opposite the 90° angle • Equals 2x Hypotenuse 2x Longer Side Shorter Side x

  5. 30-60-90 Triangle • Key Step *Use the side they give you to find x

  6. Example 1a • Given the shorter side, find the other side lengths • Shorter side is opposite the 30° • Reminder, this side is x • For this problem, x=4 • Longer Side = • Since x=4, this side is • Hypotenuse = 2x • 2(4) = 8 30° 60° 4

  7. Example 1b • Given the shorter side, find the other side lengths • Shorter side is opposite the 30° • Reminder, this side is x • For this problem, x=6 • Longer Side = • Since x=6, this side is • Hypotenuse = 2x • 2(6) = 12 30° 60° 6

  8. Example 2a • Given the longer side, find the other side lengths • Longer side is opposite the 60° • Reminder, this side is • Solve the one-step equation • Divide both sides by • X=2.8867 x=2.89 • Shorter Side = x • Since x=2.89, this side is 2.89 • Hypotenuse = 2x • 2(2.89) = 5.78 30° 5 60°

  9. Example 2b • Given the longer side, find the other side lengths • Longer side is opposite the 60° • Reminder, this side is • Solve the one-step equation • Divide both sides by • X=4.04 • Shorter Side = x • Since x=4.04, this side is 4.04 • Hypotenuse = 2x • 2(4.04) = 8.08 30° 7 60°

  10. Example 3a • Given the hypotenuse, find the other side lengths • Hypotenuse is opposite the 90° • Reminder, this side is 2x • Solve the one-step equation 2x = 35 • Divide both sides by 2 • X= 17.5 • Shorter Side = x • Since x=17.5, this side is 17.5 • Longer Side = • Since x=17.5, this side is 30° 35 60°

  11. Example 3b • Given the hypotenuse, find the other side lengths • Hypotenuse is opposite the 90° • Reminder, this side is 2x • Solve the one-step equation 2x = 24 • Divide both sides by 2 • X= 12 • Side opposite 30° = x • Since x=12, this side is 12 • Side opposite 60° = • Since x=12, this side is • Given the hypotenuse, find the other side lengths • Hypotenuse is opposite the 90° • Reminder, this side is 2x • Solve the one-step equation 2x = 24 • Divide both sides by 2 • X= 12 • Side opposite 30° = x • Since x=12, this side is 12 • Side opposite 60° = • Since x=12, this side is 30° 24 60°

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