http://www.ck12.org Chapter 8. Right Triangle Trigonometry
Solution:Let’s set up a proportion.
shorter leg in 4 SV T
shorter leg in 4 RST=
hypotenuse in 4 SV T
hypotenuse in 4 RST
4
x=
x
20
x^2 = 80
x=√
80 = 4
√
5
Example 4:Find the value ofyin 4 RSTabove.
Solution:Use the Pythagorean Theorem.
y^2 +(
4
√
5
) 2
= 202
y^2 + 80 = 400
y^2 = 320
y=√
320 = 8
√
5
The Geometric Mean
You are probably familiar with the arithmetic mean, whichdivides the sumofnnumbers byn. This is commonly
used to determine the average test score for a group of students.
The geometric mean is a different sort of average, which takes thenthroot of the productofnnumbers. In this text,
we will primarily compare two numbers, so we would be taking the square root of the product of two numbers. This
mean is commonly used with rates of increase or decrease.
Geometric Mean:The geometric mean of two positive numbersaandbis the numberx, such thatax=xborx^2 =ab
andx=
√
ab.Example 5:Find the geometric mean of 24 and 36.
Solution:x=
√
24 · 36 =
√
12 · 2 · 12 · 3 = 12
√
6
Example 6:Find the geometric mean of 18 and 54.
Solution:x=
√
18 · 54 =
√
18 · 18 · 3 = 18
√
3
Notice that in both of these examples, we did not actually multiply the two numbers together, but kept them separate.
This made it easier to simplify the radical.