Special Right Triangles

1
Special Right Triangles

• Work with a partner.
• Construct and cut out a square.
• Fold the square along the diagonal to form an
  isosceles right triangle.
• Measure each leg and each angle of the triangle.
• Use the Pythagorean theorem to determine the
  length for the hypotenuse.
• Use a calculator to divide the length of the
  hypotenuse by
• Repeat the above steps for several other squares.

2
Describe a method for finding the length of the
hypotenuse of a right isosceles triangle if you
know the length of its legs.
3
Construct an equilateral triangle. Cut out the
triangle. Fold the triangle to form a right
triangle. Measure each side and each angle of
the right triangle. Repeat the above steps for
several other equilateral triangles. b. What is
the relationship between the shortest side and
the angle having the smallest measure? c. What is
the relationship between the length of the
hypotenuse and the length of the shortest side?
4
The triangle formed in the first activity above
is called a 450-450- right triangle. The triangle
in the second activity is called a 300-600 right
triangle. The relationships you discovered above
are true for any 450-450 or a 300-600- right
triangle.
5
In a 450 - 450 right triangle, you can find the
length of the hypotenuse by multiplying the
length of a leg by Find the length of AC in
ABC.
450
5
c a c 5 5 7.071067812 The
length of AC is about 7.1 cm
450
6
In a 300- 600 right triangle, the length of the
side opposite the 300 angle is one-half of the
hypotenuse.
300
18
600
7
Find the length of PQ in PQR A ½ c A ½
(12) A 6 the length of PQ is 6 inches
600
12 inches
a
300
8
Also, in a 300 600 right triangle, you can find
the length of the side opposite the 600 angle by
multiplying the length of the other leg by .
600
18
9
300
9
9
Large doors, like those on barns and airplane
hangars, are often reinforced with a diagonal
brace to prevent warping. A barn door is designed
so that the brace forms a 300 angle as shown. If
the width of the door is 7 feet, how high is the
door?
300
7 feet
10
The brace forms two congruent right triangles.
Draw a model of one triangle to find the
measures. Let a be the measure of the side
opposite the 300 angle and b be the measure of
the side opposite the 600 angle. b a b
7 B 12.1 The door is about 12 feet
high.
300
7 feet