http://www.ck12.org Chapter 8. Right Triangle Trigonometry
y^2 +(
4
√
5
) 2
= 202
y^2 + 80 = 400
y^2 = 320
y=√
320 = 8
√
5
3.x=
√
18 · 54 =
√
18 · 18 · 3 = 18
√
3
- Use the Geometric Mean Theorems to solve forxandy.
20
x=
x
3515
y=
y
35
x^2 = 20 · 35 y^2 = 15 · 35
x=√
20 · 35 y=√
15 · 35
x= 10√
7 y= 5√
21
You could also use the Pythagorean Theorem to solve fory, oncexhas been solved for.
(
10
√
7
) 2
+y^2 = 352
700 +y^2 = 1225
y=√
525 = 5
√
21
Either method is acceptable.
Practice
Use the diagram to answer questions 1-4.
- Write the similarity statement for the three triangles in the diagram.
- IfJM=12 andML=9, findKM.
- FindJK.
- FindKL.
Find the geometric mean between the following two numbers. Simplify all radicals.
- 16 and 32
- 45 and 35
- 10 and 14
- 28 and 42
- 40 and 100
- 51 and 8
Find the length of the missing variable(s). Simplify all radicals.
11.