Download 1 2 2t - Northwest School District

Chapter 1--Section 1 (day 2)
Place the side lengths next to the sides of the triangle.
30
2
√3
60
1
30
So, using your knowledge of similar figures,
find the missing side lengths.
60
2
Therefore...
30
2t
t√3
60
t
" 30 - 60 - 90 " triangle
In any right triangle in which the two acute angles
are 30 and 60, the longest side (hypotenuse) is
twice the shortest side (opposite smallest angle)
and the side of medium length (opposite the
middle angle of 60 ) is √3 times the shortest side.
A
30
30
2t
t√3
60
t
b
C
c
a
60
B
example 1
Find the other two lengths.
a. shortest side = 4
b. longer leg = 6
c. longest side (hypotenuse) = 7
If two sides of a right triangle are
1, what's the length of the third
side?
1
1
What are the other two angle
measures?
" 45 - 45 - 90 " triangle
If the two acute angles in a right triangle are both 45,
then the two shorter sides (legs) are equal and the
longest side (hypotenuse) √2 times as long as the
shorter sides.
t√2
t
t
B
t√2
45
c
t
45
45
a
45
t
A
b
C
example 2
Find the other two lengths.
a. a leg length = 6
b. hypotenuse = 3