*you will be able to find the lengths of sides of special ...€¦ · 30-60-90 right triangle 1 2...
TRANSCRIPT
*You will be able to find the lengths of sides of special
right triangles
45-45-90
And
30-60-90
904545
906030
2:1:1
2:3:1
Leg:Leg:Hypotenuse
Short Leg:Long Leg:Hypotenuse
2:: xxx
xxx 2:3:
In a 45-45-90 triangle…
We will use a reference triangle to set up a proportion then solve.
45-45-90 Right Triangle
1
1This is our reference triangle for the 45-45-90.
2
45
45
45-45-90 Right Triangle
x
x
2x
45
45
3
3
x
1
1
3
1
x
EX: 1 Solve for x Let’s set up a proportion by
using our reference triangle.
2
2
3 2x
5
5
x
1
1
5
1
x
2
2
5 2x
EX: 2 Solve for x
x
3
1
1
x
1
3 22
45
EX: 3 Solve for x
x 3
2x
3
2
2
2
x 3 2
2
30-60-90 Right Triangle
1
2
30
60
This is our reference triangle for the 30-60-90 triangle.
3
We will use a reference triangle to set up a proportion then solve.
30-60-90 Right Triangle
x2x
30
60
3x
60
30
x
y
8
x
1
8
2
y 8
23
2 8x
4x
8 3 2y
4 3 y
12
3
30
60
Ex: 1
60
30
x
24
Solve for x
24
2
x
1
12
3
30
60
2x = 24
x = 12
Ex: 2
60
30
x
14
14
2
x
1
12
3
30
60
2x = 14
x = 7
Ex: 3
y
14
2
y
3
2y = 14 3
y = 7 3
60
30
x
x
1
12
3
30
60
x = 5
Ex: 4
y
y
5 3
5 3
3 2
5 3
3
y = 10