Area

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Special Right Triangles 5.5
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• Derive the leg lengths of special right triangles.

• Apply the ratios of the legs of special right
  triangles to find missing information.

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Consider a square with sides X.
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Take a closer look at the triangle ABC, its a
Right Triangle!
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Applying the Pythagorean Theorem, we obtain the
length of our diagonal .
Since side lengths are not negative
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Consider an equilateral triangle.
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Now, represent the lengths of our equilateral
triangle by 2X.
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Weve created a 30-60-90 triangle.
We need to determine the length of one of our
legs, its represented by the ?
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Using the Pythagorean Theorem,
Since side lengths are not negative
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Finding Side Lengths in a 45- 45º- 90º Triangle
Find the value of x. Give your answer in simplest
radical form.
By the Triangle Sum Theorem, the measure of the
third angle in the triangle is 45. So it is a
45-45-90 triangle with a leg length of 8.
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Find the value of x. Give your answer in simplest
radical form.
Simplify.
x 20
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Find the value of x. Give your answer in simplest
radical form.
The triangle is an isosceles right triangle,
which is a 45-45-90 triangle. The length of
the hypotenuse is 5.
Rationalize the denominator.
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Find the value of x. Give your answer in simplest
radical form.
The triangle is an isosceles right triangle,
which is a 45-45-90 triangle. The length of
the hypotenuse is 16.
Rationalize the denominator.
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Find the values of x and y. Give your answers in
simplest radical form.
Hypotenuse 2(shorter leg)
22 2x
Divide both sides by 2.
11 x
Substitute 11 for x.
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Find the values of x and y. Give your answers in
simplest radical form.
Rationalize the denominator.
Hypotenuse 2(shorter leg).
y 2x
Simplify.
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Find the values of x and y. Give your answers in
simplest radical form.
Hypotenuse 2(shorter leg)
Divide both sides by 2.
y 27
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Find the values of x and y. Give your answers in
simplest radical form.
y 2(5)
Simplify.
y 10
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Find the values of x and y. Give your answers in
simplest radical form.
Hypotenuse 2(shorter leg)
24 2x
Divide both sides by 2.
12 x
Substitute 12 for x.
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Find the values of x and y. Give your answers in
simplest radical form.
Rationalize the denominator.
Hypotenuse 2(shorter leg)
x 2y
Simplify.
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An ornamental pin is in the shape of an
equilateral triangle. The length of each side is
6 centimeters. Josh will attach the fastener to
the back along AB. Will the fastener fit if it is
4 centimeters long?
The equilateral triangle is divided into two
30-60-90 triangles.
The height of the triangle is the length of the
longer leg.
Find the length x of the shorter leg.
Hypotenuse 2(shorter leg)
6 2x
3 x
Divide both sides by 2.
Find the length h of the longer leg.
The pin is approximately 5.2 centimeters high. So
the fastener will fit.
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What if? A manufacturer wants to make a larger
clock with a height of 30 centimeters. What is
the length of each side of the frame? Round to
the nearest tenth.
Step 1 The equilateral triangle is divided into
two 30º-60º-90º triangles.
The height of the triangle is the length of the
longer leg.
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Step 2 Find the length x of the shorter leg.
Rationalize the denominator.
Step 3 Find the length y of the longer leg.
y 2x
Each side is approximately 34.6 cm.
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Find the exact answer of the missing side.
c.
b.
a.
e.
f.
d.
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Find the exact answer of the missing side.
y
x
b.
c.
a.
e.
f.
d.
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Find the exact answer of the missing side.
b.
c.
a.
f.
d.
e.
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Find the exact answer of the missing side.
b.
c.
a.
60?
x
x
f.
d.
e.
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Find the exact answer of the missing side.
y
x
b.
c.
a.
d.
f.
e.
30
a.
b.
c.
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Memorize these formulas.
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Assignment
Day 1 Mixed Special Right Triangles Day 2
30-60-90 45-45-90 Front