• Jun 17th 2013, 03:19 PM
TrimHonduras

Find the remaining sides of a 30° — 60° — 90° triangle if the side opposite 60° is 21.

The longest side is:

and shortest side is:

Thanks
• Jun 17th 2013, 03:37 PM
emakarov
Do you know about the tangent function?
• Jun 17th 2013, 03:49 PM
Plato
Quote:

Originally Posted by TrimHonduras
Find the remaining sides of a 30° — 60° — 90° triangle if the side opposite 60° is 21.
The longest side is:
and shortest side is:

If $\displaystyle c>a>b$ are the lengths of the sides, then you know that $\displaystyle c^2=a^2+b^2$.

What is $\displaystyle a=~?$

Moreover, as reply #2 suggests, $\displaystyle \tan(60^o)=\frac{a}{b}~.$
• Jun 17th 2013, 04:40 PM
HallsofIvy
More fundamentally, you can think of a right triangle with angle 60 degrees as half of an equilateral triangle. If the length of the hypotenuse is s (the length of each of the three sides of the equilateral triangle), then one side has length s/2 (half of the side of the equilateral triangle) and, by the Pythagorean theorem, the other side (an altitude of the equilateral triangle and so the side of the right triangle opposite the 60 degree angle) has length $\displaystyle s\sqrt{3}/2$.

The side opposite the 60 degree angle is 21 so $\displaystyle s\sqrt{3}/2= 21$. Solve for s and so determine the lengths of the other two sides.
• Jun 17th 2013, 04:49 PM
Soroban
Hello, TrimHonduras!

Quote:

Find the remaining sides of a 30°-60°-90° triangle if the side opposite 60° is 21..

The longest side is: ___

The shortest side is: ___

We are expected to know that the sides of a 30-60-90 triangle
. . are in the ratio $\displaystyle 1:\sqrt{3}:2$

We have a 30-60-90 triangle with sides in the ratio $\displaystyle a:21:c$

Can you find $\displaystyle a$ and $\displaystyle c$ ?