Question

find the missing angle and side measures of the triangle. The triangle has one angle that measures 90 degrees, and the other two angles are unknown. The two legs of the triangle measure 1 and "The square root of 3", the hypotenuse is unknown. Please find the measure of the missing angles and the hypotenuse. SHOW WORK PLEASE!!!!

Answer 1

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 $\sqrt{3}$. Now lets apply the Pythagorean theorem: $hypotenuse= \sqrt{leg^{2}+leg^{2} }$, to find our hypotenuse:
$h= \sqrt{1^{2}+ \sqrt{3}^{2} }$
$h= \sqrt{1+3}$
$h= \sqrt{4}$
$h=2$

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 $x$.
Remember that $sin(x)= \frac{opposite.side}{hypotenuse}$, so:
$sin(x)= \frac{1}{2}$
$x=sin^{-1} ( \frac{1}{2} )$
$x=30$
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 $y$:
$y=180-(90+30)$
$y=180-120$
$y=60$

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.