Download 8-2: Special Right Triangles

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
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In an isosceles right triangle, the hypotenuse is 12.
What is the length of one (1) of the sides?
A.
6 2
B.
2 6
C.
2 4
D.
2 3
E.
3
The largest triangle is equilateral
and the segment in the interior
10
is perpendicular to the base.
Determine the values of
x
x and y.
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.
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30 – 60 – 90 Triangle
30°
x√3
2x
60°
x
Solve for x and y
x
y
60
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Solve for x and y
x
24
60
°
y
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Solve for x and y
34.64
x
60
°
y
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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
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