Trigonometry functions and radicals in denominator

[silentthread]

Somehow I get a different answer than the book.

Is it because radicals can NEVER be in the denominator, and I need to multiply it byitself to cancel out?

Example, if the denominator of a fraction is square root of 5, does that means I need to multiply both side by the square root of 5?

(see below)

 

[silentthread]

Also, if I did do that, why would 3 times the square root of 13 equall to......

"2 square root of 13"

Shouldn't the answer be...

"3 square root of 13" ?

 

[silentthread]

Sorry for the 3rd post. (picture added below to further explain questions 1 and 2)

 

[chrisr]

Hold everything!!

which angle did you reference when calculating \(\displaystyle Sin\theta\) ?

The bottom left-hand angle or the top right-corner one?

That'll sort it out as everything else is fine including your resolution of how
they wrote the answer in the book.

 

[silentthread]

I think you helped me realize something. Let me know if this is correct...

To determine the opposite, hypotenuse, and adjacent, should I use the position of theta symbol?
And NOT the right angle symbol?

 

[chrisr]

Yes, that's it!

The hypotenuse is the longest side in a right-angled triangle.
The perpendicular sides are the opposite and adjacent to one of the acute angles.

You see, the hypotenuse is always opposite the right angle.

To make calculations you can choose either of the two acute angles,
but you must correctly locate the opposite and adjacent for them.

 

[silentthread]

thanks for your help