Geometry Academic
UNIT QUESTION: What patterns
can I find in right triangles?
Standard: MM2G1, MM2G2
Today’s Question:
How do we solve 45°-45°-90°
right triangles?
Standard: MM2G1.b
You will be able to find the
lengths of sides of special
right triangles
45-45-90
And
30-60-90
In a 45-45-90 triangle…
We will use a reference triangle
to set up a proportion then solve.
45-45-90 Right Triangle
45 
2
1
45 
1
This is our reference triangle for
the 45-45-90.
45-45-90 Right Triangle
45 
x 2
x
45 
x
45  45  90



Leg:Leg:Hypotenuse
1:1: 2
x: x: x 2
EX: 1 Solve for x
a 3
x
a√2
a 3
x3 2
EX: 2 Solve for x
a 5
x
a√2
a 5
x5 2
EX: 3 Solve for x
45
3 a√2
a
a x
3 2
x
2
Extension Problem
The diagonal of a square is 12 inches. Find the area. Round
to the nearest tenth.
12 in.
Area = 72
2
in.
Extension Problem 2
Given a circle with a diameter of 12 inches,
find the length of the hypotenuse of
a right triangle with the right angle at the center.
X
12 inches
Real Life Problem
30-60-90 Right Triangle
60
2
1
30
3
This is our reference triangle for
the 30-60-90 triangle.
We will use a reference triangle
to set up a proportion then solve.
30  60  90



1: 3 : 2
x : x 3 : 2x
Short Leg:Long Leg:Hypotenuse
Ex: 1 Solve for x and y.
60
a
8
2a
x
30
y
a√3
x4
4 3y
Ex: 2
Solve for x and y
y
a√3
30
x a
2a 24
60
x4
12 3  y
Ex: 3 Solve for x and y.
30
2a 14
y a√3
60
a x
x=7
y = 7√3
Ex: 4
Solve for x and y
a
x
5 3
a√3
60
2a y
x=5
30
y = 10
Extension Problem
The altitude of an equilateral triangle is 8 inches. Find the
perimeter of the triangle.
30
°
2a
8
60
°
a√3
a
a = 4.168 in., so 2a = 9.238 in.
Perimeter = 27.71 inches
D
A
30°
30°
C
B
90 feet.
A person is standing at point A cheering on his favorite team.
Round to nearest tenth.
a) Find the height CD of the bleachers.
52.0 feet
b) Find the height of the fan at Point A from the ground. 39.0 feet
c) Find the distance AB that the fan is from the field at B. 77.9 feet
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