Warmup:Solve%20for%20y

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WarmupSolve for y
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8.2 Special Right Triangles

• LEQ What are special right triangles and how do
  we use them?

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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)

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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.

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Theorem 8-5 45-45-90 Triangle Theorem

• In a 45-45-90 triangle, the hypotenuse is v2
  times as long as each leg.

45
xv2
45
Hypotenuse leg v2
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Finding the hypotenuse in a 45-45-90 Triangle

• 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 5v3.

x
45
2v16
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Finding a leg in a 45-45-90 Triangle

• Ex. 3 Find the value of x and y.

5
45
x
y
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Theorem 8-6 30-60-90 Triangle Theorem

• In a 30-60-90 triangle
• the hypotenuse is twice as long as the shorter
  leg
• the longer leg is v3 times as long as the shorter
  leg.

60
30
xv3
Hypotenuse 2 (shorter leg) Longer leg
(shorter leg) v3
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Alternatives? OF COURSE!!

• If you dont care for shortcuts, you may
  memorize

60
2
45
1
v2
1
30
v3
45
1
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Finding side lengths in a 30-60-90 Triangle

• Ex. 1 Find the values of s and t and the right.
• Ex. 2 Find the value of each variable.

60
30
60
8
x
30
y
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Real World Connection

• The yield sign is an equilateral triangle. It
  has a height of 18v3.
• Find x and y.

y inch.
18v3
x inch.