CK-12-Pre-Calculus Concepts

4.3. Special Right Triangles http://www.ck12.org

2 x= 2 √ 2

x=

√

2

x

√

3 =

√

2 ·

√

3 =

√

6

3. The other sides are 9 and 6

√

3.

TABLE4.6:

30 60 90

x x

√

3 2 x

3 √ 3

x= 3

√

3

2 x= 6 √ 3

x

√

3 = 3

√

3 ·

√

3 = 9

Practice

For 1-4, find the missing sides of the 45-45-90 triangle based on the information given in each row.

TABLE4.7:

Problem Number Side Opposite 45◦ Side Opposite 45◦ Side Opposite 90◦

1. 3


2. 7.2


3. 16


4. 5 √ 2

For 5-8, find the missing sides of the 30-60-90 triangle based on the information given in each row.

TABLE4.8:

Problem Number Side Opposite 30◦ Side Opposite 60◦ Side Opposite 90◦

5. 3 √ 2


6. 4


7. 15


8. 12 √ 3

Use the picture below for 9-11.