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8-2: Special Right Triangles

G1.2.4: Prove and use the relationships among the side lengths and the angles of 30°- 60°- 90° triangles and 45°- 45°- 90° triangles.

L1.1.6: Explain the importance of the irrational numbers √2 and √3 in basic right triangle trigonometry, the importance of π because of its role in circle relationships, and the role of e in applications such as continuously compounded interest.

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Isosceles Right Triangles

If a right triangle is isosceles, then it has 2 ___________ _________ and 2 ___________ __________. This means the measure of each acute angle must be ______. Thus another way to refer to Isosceles Right Triangles is as ___________ right triangles.

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45 - 45 - 90 Right Triangles

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The triangle below is an isosceles right triangle. What is the length of the hypotenuse? Calculate your answer 2 different ways.

6

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If one leg of an isosceles right triangle measures 15 feet, what is the perimeter of the triangle?

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What is the perimeter of the square?

8 2

In an isosceles right triangle, the hypotenuse is 12. What is the length of one (1) of the sides?

A.

B.

C.

D.

E.

26

62

42

32

3

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The largest triangle is equilateral

and the segment in the interior

is perpendicular to the base.

Determine the values of

x and y.

10

x

y

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30 -60 - 90 Right Triangles

When we cut an equilateral triangle with one altitude, we form 2 congruent right triangles each with one 30 and one 60 degree angle.

These are called 30 - 60 - 90 right triangles.

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30 - 60 - 90 Right Triangle Theorem

If the shortest leg of a 30-60-90 right triangle is x units long, then the hypotenuse is 2x units long and the longer leg is x times the square root of 3 units long.

30 – 60 – 90 Triangle

60°

30°

x

2xx√3

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Solve for x and y

60

18

xy

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Solve for x and y

60°

y

x24

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Solve for x and y

60°

y

34.64 x

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An altitude of an equilateral triangle is 8.3 meters. Find the perimeter of the triangle to the nearest tenth of a meter.

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Assignment

Pages 409 - 410,# 11 - 21 (odds), 33