D.N.A.
Find the missing side of the triangle.
1)
2)
7
x
5
7
3)
20
x
15
5
x
Special Right Triangles
Chapter 8.3
DNA
NUMBER SENSE
STATISTICS, DATA, AND PROB.
ALGEBRA AND FUNCTIONS
MEASUREMENT AND GEOMETRY
MATHEMATICAL REASONING
ALGEBRA 1
Find the length of the Hypotenuse
c  5 5
2
c  25  25
c  50
c  25 2
c5 2
2
45o
5
45o
5
2
2
Find the length of the Hypotenuse
c x x
2
c  2x
2
c x 2
cx 2
2
45o
x
45o
x
2
2
o
o
o
45 -45 -90
Triangle
• The hypotenuse is 2 times as long as each leg.
• x, x, x(2)
x 2
x
x
Find the missing sides
7 2
7
7
Find the missing sides
8 2
8
8
Find the missing sides
10
5 2
5 2
x 2  10
10
x
2
10 2 10 2
x


2
2 2
x5 2
Find the length of the missing side
10  5  x
2
x  100  25
x  75
x  25 3
x5 3
2
30o
10
5 3
60o
5
2
2
Find the length of the missing side
( 2 x)  x  b
2
2
2
4x  x  b
2
2
3x  b
2
b  3x
2
b x 3
bx 3
2
30o
2x
x 3
60o
x
2
2
o
o
o
30 -60 -90
Triangle
• Legs
x, x3
• Hypotenuse 2x
30o
2x
x 3
60o
x
Find the missing side lengths
30o
16
8 3
60o
8
Find the missing side lengths
30o
12
6 3
60o
6
Find the missing side lengths
30o
5 3 3
5 9  5  3  15
10 3
60o
5 3
Find the missing side lengths
30o
16 3
3
8
60o
8 3
3
x 3 8
8
x
3
8
3 8 3
x


3
3 3
16 3
2x 
3
Find the missing side lengths
30o
8 3
12
60o
4 3
x 3  12
12
x
3
12 3 12 3
x


3
3 3
4 3
2x  8 3
Find BC.
A. 4 in.
B. 8 in.
C.
1.
2.
3.
4.
0%
D. 12 in.
A
B
C
D
A
B
C
D
Special Triangles in a Coordinate Plane
Copy this problem!
COORDINATE GEOMETRY ΔWXY is a
30°–60°–90° triangle with right angle X
and
as the longer leg.
Graph points X(–2, 7) and Y(–7, 7), and
locate point W in Quadrant III.
Special Triangles in a Coordinate Plane
Graph X and Y.
lies on a horizontal gridline of the
coordinate plane. Since
will be perpendicular to
it lies on a vertical gridline. Find the length of
Short leg
60
YX=5
II
30 
III
I
Long leg
XW = 5 3  8.7 units
Coordinates:
W
IV
(-2, -1.7)
COORDINATE GEOMETRY ΔRST is a 30°–60°–90°
triangle with right angle R and
as the longer leg.
Graph points T(3, 3) and R(3, –6) and locate point S in
Quadrant III. What are the approximate coordinates
of S?
A. (–4.8, –6)
B. (–2.2, –6)
C. (–1.5, –6)
D. (–12.6, –6)
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
Homework
Chapter 8.3
• pp. 451
#1 – 5, 8 - 15,
34, 36, 40,
42, 44 and 48