Question

Trigonometry question?

This was on my recent skills check and although I've already finished it, it's still bugging me a little bit.

I was told to find the sine, cosine, and tangent of angle A of this triangle:

http://puu.sh/5lL98.png

From this illustration you can clearly tell this:

opposite is 12ft
adjacent is 22ft
hypotenuse is not given

The only one you can find with these terms is tangent, so tangent is 12/22 or 6/11.

I can find the hypotenuse by using a^2 + b^2 = c^2, fill in the variables and you get
12^2 + 22^2 = c^2
c^2 = 628

square root of 628 is about 25.

That being said, I can rearrange my data and solve for sine and cosine.

Opposite: 12
Adjacent: 22
Hypotenuse: 25
Sine of angle A = 12/25
Cosine of angle A = 22/25
Tangent of angle A =6/11

HOWEVER...

The options given for this question were these:

http://puu.sh/5lLq1.png

I managed to get this right by guessing, but I'm confused as to where the square root of 157 came from. This has been bothering me for an hour. Someone explain!

Answer 1

math teachers are a pain, lets do it

Answer 2

@satellite73 I have absolutely NO clue how this works. Hahaha. Whoever made these questions should be fired.

Answer 3

..... Disappointed in my lack of acknowledging this.

Answer 4

You win @satellite73

Answer 5

first off, lets reduce, because all the ratios will be the same, so you don't need \(12,22\) when \(6,11\) will do
that should be clear, as when you found the tangent

Answer 6

then the hypotenuse is \[\sqrt{11^2+6^2}=\sqrt{121+36}=\sqrt{157}\]

Answer 7

And suddenly, it all makes sense.

Answer 8

then instead of writing
\[\sin(A)=\frac{6}{\sqrt{157}}\] like a normal person, they rationalized the denominator and wrote
\[\sin(A)=\frac{6\sqrt{157}}{157}\]

Answer 9

you would have gotten the same thing without reducing, but you would have had to write the radical in simplest radical form, then reduced, so it is a lot easier (clearly) to reduce first
you good from there?

Answer 10

Yep. Thank you. Makes a ton more sense now haha.

Answer 11

yw