# missing angle

• Feb 28th 2011, 01:40 PM
andyboy179
missing angle
hi,
i need to find the missing angle of this triangle marked X:

Attachment 20997
would it be correct to work it out like this:

cos82= 23/X
23=Xxcos82
23/cos82= 165.26
X=165.26??

if this is incorrect could you please let me know how i can improve on this to make it correct!

thanks!
• Feb 28th 2011, 01:52 PM
Quacky
Not quite. $Cos(82)=\frac{x}{23}$

Remember 'Sohcahtoa' - $Sin = \frac{Opp}{Hyp}; Cos = \frac{Adj}{Hyp}; Tan = \frac{Opp}{Adj}$

Where 'adj' = the line adjacent to the angle, 'opp' = the line opposite the angle, and 'hyp' is the hypotenuse - the longest side.

I'm sure you can solve from there.

Edit:I assumed you meant that you wanted to find X. If it's the missing angle you need, then see below.
• Feb 28th 2011, 01:53 PM
topsquark
Quote:

Originally Posted by andyboy179
hi,
i need to find the missing angle of this triangle marked X:

Attachment 20997
would it be correct to work it out like this:

cos82= 23/X
23=Xxcos82
23/cos82= 165.26
X=165.26??

if this is incorrect could you please let me know how i can improve on this to make it correct!

thanks!

The sum of the interior angles of a triangle is 180 degrees. You have an angle of 82 degrees and a right angle. How do you find the remaining angle?

-Dan
• Feb 28th 2011, 02:01 PM
andyboy179
Oh yes, well spotted quacky I need to find X. Quacky it must be cos because there is nothing opposite the angle 82.
• Feb 28th 2011, 02:05 PM
Quacky
Quote:

Originally Posted by andyboy179
Oh yes, well spotted quacky I need to find X. Quacky it must be cos because there is nothing opposite the angle 82.

I agree with you there. But according to your diagram, the adjacent angle is the one marked $x$, and the hypotenuse is 23. Look carefully at my correction.
• Feb 28th 2011, 02:15 PM
andyboy179
I'm confused, I know adj is X and hyp is 23
• Feb 28th 2011, 02:20 PM
Quacky
Quote:

Originally Posted by andyboy179
I'm confused, I know adj is X and hyp is 23

So $Cos(82)=\displaystyle\frac{x}{23}$, as I said above. You wrote initially: $Cos(82)=\displaystyle\frac{23}{x}$

It was just a small mistake, but you get very different answers.
• Feb 28th 2011, 02:36 PM
andyboy179
Oh I see and 23 being the biggest side would mean X is smaller than 23. So X = 3.2?
• Feb 28th 2011, 02:45 PM
Quacky
Quote:

Originally Posted by andyboy179
Oh I see and 23 being the biggest side would mean X is smaller than 23. So X = 3.2?

Yeah, that's right.
• Feb 28th 2011, 08:06 PM
Wilmer
Quote:

Originally Posted by andyboy179
23=Xxcos82

Please use * to indicate multiplication, NOT x ; 23 = X * cos(82)