http://www.ck12.org Chapter 8. Right Triangle Trigonometry
Example C
Find the measure ofx.
Think of this trapezoid as a rectangle, between a 45-45-90 triangle and a 30-60-90 triangle.
From this picture,x=a+b+c. First, finda, which is a leg of an isosceles right triangle.
a=24
√
2
·
√
2
√
2
=
24
√
2
2
= 12
√
2
a=d, so we can use this to findc, which is the shorter leg of a 30-60-90 triangle.
c=12
√
2
√
3
·
√
3
√
3
=
12
√
6
3
= 4
√
6
b=20, sox= 12
√
2 + 20 + 4
√
- Nothing simplifies, so this is how we leave our answer.
Watch this video for help with the Examples above.
MEDIA
Click image to the left for more content.CK-12 Foundation: Chapter8306090RightTrianglesB
Vocabulary
Aright triangleis a triangle with a 90◦angle. A30-60-90 triangleis a right triangle with angle measures of
30 ◦, 60 ◦, and 90◦.
Guided Practice
- Find the length of the missing sides.
- Find the value ofxandy.
3.xis the hypotenuse of a 30-60-90 triangle andyis the longer leg of the same triangle. The shorter leg has a length
of 6.
Answers:
- We are given the hypotenuse. 2x=20, so the shorter leg,f=10, and the longer leg,g= 10
√
3.
- We are given the hypotenuse.
2 x= 15√
6
x=