http://www.ck12.org Chapter 8. Right Triangle Trigonometry
Draw a picture.
We know half of a square is a 45-45-90 triangle, so 10=s
√
2.
s√
2 = 10
s=10
√
2
·
√
2
√
2
=
10
√
2
2
= 5
√
2
Watch this video for help with the Examples above.
MEDIA
Click image to the left for more content.CK-12 Foundation: Chapter8454590RightTrianglesB
Vocabulary
Aright triangleis a triangle with a 90◦angle. A45-45-90 triangleis a right triangle with angle measures of
45 ◦, 45 ◦, and 90◦.
Guided Practice
- Find the length of the missing sides.
- Find the length ofx.
3.xis the hypotenuse of a 45-45-90 triangle with leg lengths of 5
√
3.
Answers:
- Use thex:x:x
√
2 ratio.AB= 9√
2 because it is equal toAC. So,BC= 9√
2 ·
√
2 = 9 · 2 =18.
- Use thex:x:x
√
2 ratio. We need to solve forxin the ratio.12
√
2 =x√
2
12 =x3.x= 5
√
3 ·
√
2 = 5
√
6
Practice
- In an isosceles right triangle, if a leg isx, then the hypotenuse is __.
- In an isosceles right triangle, if the hypotenuse isx, then each leg is __.
- A square has sides of length 15. What is the length of the diagonal?
- A square’s diagonal is 22. What is the length of each side?
- A square has sides of length 6
√
- What is the length of the diagonal?
- A square has sides of length 4
√
- What is the length of the diagonal?