Point P ( √ 3,−1 ) is on the terminal arm of an angle x in standard position. Determine the measure of the related acute angle.

Answer 1

Setting up a diagram to picture the angle and corresponding triangle will help. The related acute angle of the triangle will lie in the 4th quadrant. Since the horizontal leg of the triangle has length √ 3 and the vertical leg has length 1, by use of the Pythagorean Formula we can determine that the hypotenuse of the triangle is 2 units long. Since one of the legs is half this length, this is a 30-60-90 right triangle, and since the leg that is half of the hypotenuse is opposite the acute angle in question, that angle must be the 30° angle.