62 degrees
To find angles when two sides are given to us we got to know which sides they have given us, in this case, they gave us the adjacent and the hypotenuse and are asking us to find the angle theta so we use function cos in our calculator.
adjacent is the angle that connects both the 90-degree angle and the given angle and the hypotenuse is the longest side of the triangle.
adjacent or side g = 9
hypotenuse or side h = 19
to find the angle we use the following formula:
adjacent = hypotenuse × cosø
side g = side h × cosø
9 = 19 × cosø
we then move the 19 from the multiplication to a division on the left side of the equation.
9/19 = cosø
0.4736842105 = cosø
so if cosø = 9/19
then ø = cos^-1 (9/19)
angle ø = 61.72628637
to the nearest decimal place is ø= 62 degrees.