## Trig right triangle solving question How do you know if you should pick tan40 degrees

Trig right triangle solving question How do you know if you should pick tan, cot, etc for the last part?
if b = 2 , A =40 , find a,c, and B
I found all of them except for c , how do you get c
There's a part almost at the end that goes like tan40 degrees = a/2 and Cos 40 degrees = 2/c
Why do you know to pick Cos 40 , why not tan40 or cot of 40 for that last part there?

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 Recognitions: Science Advisor What "last part there"? You haven't included whatever you're talking about in your post. A guess about the use of cosine: To find an unknown with a trig function, you must have an equation that has the unknown in it along with other known information. If you want to find c and cosine involves c, use cosine. There is often more than one way to solve for an unknown. If c is the hypotenuse you can also use $$c^2 = a^2 + b^2$$ to solve for it after you find b.

 Quote by land_of_ice Trig right triangle solving question How do you know if you should pick tan, cot, etc for the last part? if b = 2 , A =40 , find a,c, and B I found all of them except for c , how do you get c There's a part almost at the end that goes like tan40 degrees = a/2 and Cos 40 degrees = 2/c Why do you know to pick Cos 40 , why not tan40 or cot of 40 for that last part there?
Can you upload a picture that explains this?

My guess is, although Stephen Tashi is right, it's usually best to only use values given in a question if you can, just in case your values calculated in other parts of the question are wrong, which could cause confusion if you get odd answers later on.

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## Trig right triangle solving question How do you know if you should pick tan40 degrees

The convention is that, in a triangle, sides labeled a, b, c are opposite angles labeled A, B, C respectively.

And, in right triangles, by convention, C is the right angle and c is the hypotenuse.

Back when you first learned about trig functions you were supposed to have learned something like:
sine= opposite side/hypotenuse,
cosine= near side/hypotenuse
tangent = opposite side/near side

Given angle A and side b, you think- a is the side opposite angle A and b is the other leg, the side "near" angle A so the appropriate formula is "tangent= opposite side/near side": tan(A)= a/b or tan(40)= a/2. Then solve for a.

To find c, given only angle a and angle b, you think, c is the hypotenuse and b is the "near" side to A so the appropriate formula is "cosine= near side over hypotenuse":
cos(A)= b/c or cos(40)= 2/c. Then solve for c.

Of course, if, at this point, you have already solved for a, you could think "sine= opposite side over hypotenuse": sin(40)= a/c. Or, as Stephen Tashi said, you could use $c^2= a^2+ b^2$. However, I agree with sjb-2812 that it is better to use the initially given values- you will not propagate arthmetic errors.

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