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Warmup:Solve for y

Warmup:Solve for y. 8.2 Special Right Triangles. LEQ: What are special right triangles and how do we use them?. The “root” of it all…. Calculate the value of each hypotenuse in a triangle as a reduced radical… Do you notice a trend? Is there an easier way to calculate (shortcuts)?.

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Warmup:Solve for y

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  1. Warmup:Solve for y

  2. 8.2 Special Right Triangles LEQ: What are special right triangles and how do we use them?

  3. The “root” of it all… Calculate the value of each hypotenuse in a triangle as a reduced radical… Do you notice a trend? Is there an easier way to calculate (shortcuts)? (hint: label sides with numbers)

  4. Side lengths of Special Right Triangles • Right triangles whose angle measures are 45°-45°-90° or 30°-60°-90° are called special right triangles. • The theorems that describe these relationships of side lengths of each of these special right triangles follow….

  5. In a 45°-45°-90° triangle, the hypotenuse is √2 times as long as each leg. Theorem 8-5: 45°-45°-90° Triangle Theorem 45° x√2 45° Hypotenuse = leg ∙ √2

  6. Ex 1: Find the value of x at the right. Ex 2: Find the length of the hypotenuse of a 45-45-90 triangle with legs of length 5√3. Finding the hypotenuse in a 45°-45°-90° Triangle x 45° 2√16

  7. Ex. 3 Find the value of x and y. Finding a leg in a 45°-45°-90° Triangle 5 45° x y

  8. In a 30°-60°-90° triangle: the hypotenuse is twice as long as the shorter leg the longer leg is √3 times as long as the shorter leg. Theorem 8-6: 30°-60°-90° Triangle Theorem 60° 30° x√3 Hypotenuse = 2 ∙ (shorter leg) Longer leg = (shorter leg) ∙ √3

  9. Alternatives? OF COURSE!! If you don’t care for shortcuts, you may memorize… 60 2 45 1 √2 1 30 √3 45 1

  10. Ex. 1 Find the values of s and t and the right. Ex. 2 Find the value of each variable. Finding side lengths in a 30°-60°-90° Triangle 60° 30° 60° 8 x 30° y

  11. The yield sign is an equilateral triangle. It has a height of 18√3. Find x and y. Real World Connection y inch. 18√3 x inch.

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