# Homework Help: Definition of Acute Angle

1. Jun 9, 2010

### number0

1. The problem statement, all variables and given/known data

Let u=3i+0j+k and v=i-2j+k have a common tail. Let $$\theta$$ be the acite angle

between u and v. Calculus sin$$\theta$$

2. Relevant equations

ll u x v ll = ll u ll ll v ll sin$$\theta$$

3. The attempt at a solution

First of all, I solved the problem already. To save time, I will not show my work, but show

the answer I computed:

sin$$\theta$$ = $$\frac{\sqrt{44}}{\sqrt{10}\sqrt{6}}$$

Which is equivalent to my textbook's answer:

sin$$\theta$$ = $$\sqrt{\frac{11}{15}}$$

Now my question is how do I transform the answer I computed to the textbook's answer? I

am pretty sure that it has to do with the concept of acute angles. Can anyone please

explain this to me? Thanks.

Last edited: Jun 9, 2010
2. Jun 9, 2010

### rock.freak667

√a√b = √ab

√a/√b = √(a/b)

3. Jun 9, 2010

### Office_Shredder

Staff Emeritus
An acute angle is just one that is between 0 and $$\frac{\pi}{2}$$. Draw a pair of lines forming a (smallish) angle. There are two angles really formed, the obvious small one between them, and the huge one that's about 300 degrees on the other side.

4. Jun 9, 2010

### number0

Hmmm, I see. But, I still do not know how to convert an obtuse angle to an acute angle. So

let's pretend that I have a an angle, say:

cos$$\theta$$ = $$\frac{-10}{\sqrt{22}\sqrt{42}}$$.

How do I go about converting this angle into an acute angle without using a calculator?

5. Jun 9, 2010

### vela

Staff Emeritus
It has nothing to do with the concept of acute angles. It's just algebra. Use the rules rock.freak posted to simplify the expression.