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

Do you know about the tangent function?

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, $\displaystyle \tan(60^o)=\frac{a}{b}~.$

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.

Hello, TrimHonduras!

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 $\displaystyle c$ ?