Triangle Side Lengths: Find the Third Side with 10 and 14 Units & 30° Angle

[Phanatic 12]

A triangle has sides of length 10 and 14 units respectively, and one of the non-included angles is 30 degrees. Find the possible lengths of the third side. The answers is the product of these lengths.

 

[Mark44]

A triangle has sides of length 10 and 14 units respectively, and one of the non-included angles is 30 degrees. Find the possible lengths of the third side. The answers is the product of these lengths.

This looks like a homework problem, and so should have been posted in the Homework section, in the Precalculus subsection.

What are the relevant formulas? What have you tried?

 

[Grep]

A triangle has sides of length 10 and 14 units respectively, and one of the non-included angles is 30 degrees. Find the possible lengths of the third side. The answers is the product of these lengths.

What have you tried so far? For example, do always sketch a triangle so you can see what you're working with.

I'll give you one hint to get you started. First, assign variables to your sides and angles. Say, \angle{A}, \angle{B} and \angle{C} for the angles and a, b and c for the sides. Now, here's something to ponder:
\frac{ \sin{\angle{A}}}{a} = \frac{\sin{\angle{B}}}{b}

EDIT: Oops, I didn't notice he posted it in the wrong forum. My bad.

 

[symbolipoint]

Law of Cosines! http://en.wikipedia.org/wiki/Law_of_cosines