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SPECIAL RIGHT TRIANGLES:. But first, a short video introduction on TRIANGLES:. REMEMBER THESE FACTS:. Angles are on the INSIDE of a Triangle. Sides are the LINES of a Triangle. Angles are written in degrees (90 ◦, 30◦, 45◦). All the angles in ANY Triangle always add up to 180 ◦. - PowerPoint PPT Presentation
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SPECIAL RIGHT TRIANGLES:
But first, a short video introduction on TRIANGLES:
REMEMBER THESE FACTS:
Angles are on the INSIDE of a Triangle.Sides are the LINES of a Triangle.
Angles are written in degrees (90◦, 30◦, 45◦)
All the angles in ANY Triangle always add up to 180◦
RIGHT TRIANGLE & SPECIAL RIGHT TRIANGLES:
45º
45º
60º
30º
WHY SPECIAL RIGHT TRIANGLES:
We use these 2 Special Right Triangles when we need to find the LENGTH of an unknown
side of a RIGHT TRIANGLE.
We use The PYTHAGOREAN THEOREM formula when you know TWO side lengths of
a RIGHT TRIANGLE.
We use the SPECIAL RIGHT TRIANGLE formulas when we know ONE side of either
type of SPECIAL RIGHT TRIANGLE.
Pythagorean Theorem:
a² + b² = c²
We use it when we know the length of 2 SIDES of a Right Triangle and we need to find the length of the unknown side.
a
b
c
Example of when to use the Pythagorean Theorem:
10 in
14 in
?
a² + b² = c²
What is the length of the missing side?
Example of when to use the Pythagorean Theorem:
12 in
18 in
?
a² + b² = c²
What is the length of the missing side?
Example of when to use the Pythagorean Theorem:
25 in
36 in
?
a² + b² = c²
What is the length of the missing side?
Example of when to use the Pythagorean Theorem:
14.5 in
18.5 in
?
a² + b² = c²
What is the length of the missing side?
Example of when to use the Pythagorean Theorem:
10 in
?
25 in
a² + b² = c²
What is the length of the missing side?
Example of when to use the Pythagorean Theorem:
?
18 in
64 in
a² + b² = c²
What is the length of the missing side?
What is the difference between these two triangles?:
45º
45º
You know EXACTLY what the angles are on the triangle on the LEFT.
You DON’T KNOW EXACTLY what the angles are on the triangle on the RIGHT.
Opposite Operations:
X X+ -- +C² c²
Opposite
Opposite
Opposite
Opposite
Opposite
Opposite
45 45 90 Special Right Triangle:
30 60 90 Special Right Triangle:
Practice Problem#1:
45º
45º
xx√2
x
Practice Problem#1:
60º
30º
y√3
y
2y
Practice Problem #1
a² + b² = c²
What is the length of the missing side?
Practice Problem #1
10 in
14 in
?
a² + b² = c²
What is the length of the missing side?
Template: Solving for c
a² + b² = c²
( )( ) + ( )( ) = c²
( ) + ( ) = c²
( ) = c²
√( ) = c
= c
Template: Solving for a or b
a² + b² = c²
a² + ( )( ) = ( )( )
a² + ( ) = ( )
- ( ) - ( )
a² = ( )
a = √( )
a =
Pythagorean Theorem OR
Special Right Triangles?
4in
8in
?4in
45º
?
?
45º
a² + b² = c²
Special Right Triangles
Practice Problem #1
a² + b² = c²OR
Special Right Triangles?
What is the length of the missing side?
MCAS PROBLEM EXAMPLE:
YW
T
X
V
45º
4 in
6 in
MCAS PROBLEM EXAMPLE:
YW
T
X
V
45º
4 in
6 in
MCAS PROBLEM EXAMPLE:
YW
TX
V
45º
4 in
6 in
MCAS PROBLEM EXAMPLE:
YW
T
X
V45º
4 in
6 in
When you know the WHOLE and you know a PART, how do you find out what the UNKNOWN PART is?
WHOLE - PART
UNKNOWN PART
