Finding an Angle in a Right Triangle

In a right triangle, the lengths of the two legs are 6 units and 8 units. To find the measure of the angle opposite the leg measuring 6 units, you can use trigonometric functions. Specifically, you can apply the sine function, which is defined as the ratio of the length of the opposite side to the length of the hypotenuse.

Which of the following is the approximate measure of the angle (in degrees) opposite the side measuring 6 units?

First, calculate the length of the hypotenuse using the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse ($$c$$) is equal to the sum of the squares of the other two sides: $$c^2 = a^2 + b^2$$.