Find the coordinates of point C if you know that the angle is BOC = 60 °, O is the origin

| August 8, 2021 | education

Find the coordinates of point C if you know that the angle is BOC = 60 °, O is the origin, B (-1/2; √3 / 2), and point C lies on the unit semicircle.

Consider the triangle AOB.

OA length = 1/2 cm, AB length = √3 / 2 cm.

Then, by the Pythagorean theorem OB ^ 2 = OA ^ 2 + AB ^ 2 = 1/4 + 3/4 = 4/4 = 1 cm.

Point B lies on the unit circle.

In a right-angled triangle AOB, the length of the hypotenuse OB = 2 * OA, then the angle ABO = 30, then the angle BOD = ABO = 300 as criss-crossing angles.

According to the condition, the angle BOS = 60, and since point C lies on the unit circle, then ОВ = ОС, and the triangle BOS is equilateral.

Then SD = BD = 1/2 cm, and the coordinates of the point C (1/2; √3 / 2).

Answer: The coordinates of the point are equal: С (1/2; √3 / 2).



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.