# How do you find the remaining side of a 30^circ-60^circ-90^circ triangle if the longest side is 5?

Mar 3, 2017

opposite side$= 4.33$ , adjacent side $= 2.5$

#### Explanation:

Let the top angle be $\textcolor{w h i t e}{a a a a a a a a}$ angleA=30°
Let the bottom left angle be $\textcolor{w h i t e}{a a}$ angleB=60°
Let the bottom right angle be $\textcolor{w h i t e}{a}$  angleC=90°
AB= hypotenuse side=5 given
AC= opposite side

:.(BC)/(AB)=Cos 60°

multiply L.H.S. and R.H.S. by $\frac{A B}{1}$

cancel(AB)/1 xx (BC)/cancel(AB)=(AB)/1 xx Cos60°

BC=5 xx cos60°

$B C = 5 \times 0.5$

$B C = 2.5$

(AC)/(AB)=sin60°

multiply L.H.S. and R.H.S. by $\frac{A B}{1}$

$\frac{\cancel{A B}}{1} \times \frac{A C}{\cancel{A B}} = \sin 60 \times \frac{A B}{1}$

AC=sin60° xx 5/1

$A C = 0.866025403 \times 5$

$A C = 4.330127019$

CHECK:

tan60°=(AC)/(BC)=(4.330127019)/2.5=arctan1.732050808=60°

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