Transcript Chapter 8: Right Triangles & Trigonometry

Chapter 8: Right Triangles &
Trigonometry
8.2
Special Right Triangles
Isosceles Right Triangles
• What are the angle measures of an
isosceles right triangle?
Theorem 8-5
• 45-45-90 Triangle Theorem
– In a 45-45-90 triangle, both legs are congruent and
the length of the hypotenuse is √2 times the length
of a leg
s 2
s
s
Example 1
• Find the value of h:
9
45
45
h
Example 1
• Find the value of x:
45
2 2
x
45
Example 1a
• Find the length of the hypotenuse of a 4545-90 triangle with legs of length 5√3.
Example 2
• What is the value of x?
6
x
Example 3
• A high school softball diamond is a square. The
distance from base to base is 60 feet. To the
nearest foot, how far does a catcher throw the
ball from home plate to second base?
Example 3a
• A square garden has sides 100 ft long. You
want to build a brick path along a diagonal of
the square. How long will the path be?
Theorem 8-6
• 30-60-90 Triangle Theorem
– In a 30-60-90 triangle, the length of the hypotenuse
is twice the length of the shorter leg. The length of
the longer leg is √3 times the length of the shorter
leg.
30
2x
x 3
60
x
Example 4
• Find the value of each variable:
5
d
60
30
f
Example 4a
• Find the value of each variable:
60
8
x
30
y
Homework
• p. 428
• 1-6, 9-14, 17-22