Special Right Triangles
What kind of triangle is this?
Isosceles
What are the measures
of the other two angles?
45° and 45°
Find the measure of the missing angles
12 in
5.3 in
5.3 in
12 in
X
X
Find the measure of the missing angles
12 in
5.3 in
5.3 in
12 in
X
X
The missing
angles are all
45°
The moral of the story is…
In every isosceles right triangle,
• the angles measure 45° - 45° - 90 °
• The two legs are equal in measure
AND… (this is the hard one to remember, but you
can do it)
• The hypotenuse is equal to the leg times the
square root of 2
Anatomy of a 45° - 45° - 90° triangle
45°
X√2
X
45°
X
Memorize this picture and learn how to use it!!!!
Find the length of the hypotenuse
12 in
5.3 in
5.3 in
12 in
X
X
Find the length of the hypotenuse
12 in
5.3 in
5.3 in
12 in
5.3√2
12√2
X√2
X
X
Find the length of the missing sides
x
x
8√2
y√2
45°
34√2
Find the length of the missing sides
8
34
34
8
34√2
8√2
y√2
y
45°
y
Find the measure of the missing angles
(“theta”)
°
60°
60°
°
30 °
°
Find the measure of the missing angles
(“theta”)
° = 30 °
60°
60°
° = 30 °
30°
° = 60 °
What do you notice about the lengths of
the sides?
22 cm
30 °
60°
5 in
10 in
60°
30 °
The hypotenuse is twice
as long as the side
opposite the 30° angle.
44 cm
30°
15 cm
60 °
7.5 cm
30° - 60°- 90° triangles
In every 30° - 60° - 90° triangle,
• the leg opposite the 30 ° angle is the shortest leg
• The hypotenuse is twice as long as the shortest
leg
AND… (this is the hard one to remember, but you
can do it)
• The middle leg is equal to the shortest leg times
the square root of 3
Examples of 30° - 60°- 90° triangles
5√3 in
22 cm
30 °
5 in
60°
10 in
22√3
cm
30 °
The middle length leg is
equal to the shortest leg
times the square root of
3. It is always opposite
the 60° angle.
60°
44 cm
30°
15 cm
60 °
7.5 cm
15√3
cm
Anatomy of a 30° - 60° - 90 ° triangle
30°
2X
X√3
60°
X
Memorize this picture and learn how to use it!!!!