Question

Suppose a triangle has two sides of length 2 and 5 and that the angle between these two sides is pi/3. What is the length of the third side of the triangle?

Answer 1

Surely sounds like a case of side-angle-side, doesn't it? Which trig formula would help you find the length of the third side in the quickest possible way?

Answer 2

I'd assume the one that goes:
a^2 = b^2 + c^2 - 2(b)(c)(cos(angle)) ??
I think that's correct...

Answer 3

Dear Perfectly Capable, I'd suggest you sketch this situation for yourself, if you haven't already. yes, you're absolutely correct. Bet you can now find that "angle".

Answer 4

I disagree with the "Incapable" part.

Answer 5

a^2 = 2^2 +5^2 - 2*2*5*cos(pi/3)
that's what I tried, but i'm getting the wrong answer.
and thank you :)

Answer 6

You're welcome!
We want side a. We therefore apply the formula exactly as you have typewritten it:

\[a ^{2}=b ^{^{2}}+c ^{2}-2bc*\cos A\] or

Answer 7

\[a ^{2}=(2)^{2}+(5)^2 - 2(2)(5) (\frac{ 1 }{ 2 })\]

Answer 8

a^2 = 4 + 25 - 20(cos(1.05)
a^2 = 29 - 20(1)
a^2 = 29 - 20
a^2 = 9
a = 3
That's how i did it (rounding the cos part of course), but it doesn't seem to be correct

Answer 9

why would it be 1/2?

Answer 10

Aha. It helps so much that you've shared your work.

Note that angle A is pi/3, or A = 60 degrees.

How do you normally find the sine or cosine of a given angle?

Answer 11

Use whatever method to evaluate cos (pi/3), or cos (30 degrees).

Answer 12

Very sorry, but that's cos (60 degrees).

Answer 13

oh my god... i completely forgot about converting pi/3 into degrees.
doing (pi/3)*(180/pi)=60 i got you now. i'm sorry... my mind is a mess

Answer 14

then cos(60) = 1/2

Answer 15

Note that the angle 60 degrees drawn in Q1 will have opposite side equal to Sqrt(3), adj side 1, and hyp 2. So yes, cos 60 = 1/2. You ok with that?

Answer 16

With all this info, you should now be able to find a^2, and from a^2, to find a.

Answer 17

a^2 = 2^2 + 5^2 - 2(2)(5)(1/2)
a^2 = 4 + 25 - 10(1)
a^2 = 29 - 10
a^2 = 19
a = sqrt19 which is one of the answers

Answer 18

Hope you're feeling comfortable and confident regarding this work now. Happy for having had the opp to work with you.. :)

Answer 19

I was trying to take the cosine of pi/3. I'll make sure to convert from now on. thank you very much, i get it :)

Answer 20

My great pleasure. Bye!