Since we know that the measure of one of the angles is 90°, we know that we have a right triangle with legs 1 and [tex] \sqrt{3} [/tex]. Now lets apply the Pythagorean theorem: [tex]hypotenuse= \sqrt{leg^{2}+leg^{2} } [/tex], to find our hypotenuse:
[tex]h= \sqrt{1^{2}+ \sqrt{3}^{2} } [/tex]
[tex]h= \sqrt{1+3} [/tex]
[tex]h= \sqrt{4} [/tex]
[tex]h=2[/tex]
Now that we know that the measure of the hypotenuse is 2, lets use the trig function sine to find one of the angles that we are going to call [tex]x[/tex].
Remember that [tex]sin(x)= \frac{opposite.side}{hypotenuse} [/tex], so:
[tex]sin(x)= \frac{1}{2} [/tex]
[tex]x=sin^{-1} ( \frac{1}{2} )[/tex]
[tex]x=30[/tex]
Now that we have two angles, remember that the sum of the interior angles of a triangle is 180°; lets use that to find our final angle [tex]y[/tex]:
[tex]y=180-(90+30)[/tex]
[tex]y=180-120[/tex]
[tex]y=60[/tex]
We can conclude that the measure of the hypotenuse of our triangle is 2, and the measure of its missing angles are 30° and 60° respectively.
