1) To find
we are going to use the Pythagorean equation:
where
and
are the legs of our triangle. For our picture we can infer that
and
, so lets replace those values in our equation to find
:
We can conclude that the value of
in our triangle is
12.82) To find
we are going to use the trigonometric function tangent. Remember that
. We know that the opposite side of our angle
is 8, and its adjacent side is 10, so lets replace those values in our tangent function to find
:
Since we need the measure of angle
, we are going to take inverse tangent to both sides to find it:
We can conclude that the value of
in our triangle is
38.66°3) Finally, to find
we are going to take advantage of two facts: the sum of the interior angles of a triangle is always 180°, and our triangle is a right one, so one of its sides is 90°. Therefore,
. Since we already know the value of
, lets replace it in our equation and solve for
:
We can conclude that the measure of angle
is
51.34°<span />
