In a right-angled triangle ABC (angle C = 90 degrees) AC = 10 cm, angle B = 60 degrees.

In a right-angled triangle ABC (angle C = 90 degrees) AC = 10 cm, angle B = 60 degrees. Find the distance from the vertex C to the hypotenuse AB.

1. To determine the distance from the vertex C of the triangle to the hypotenuse AB, draw the perpendicular CH from this vertex.

2. We calculate the value of the angle BAC, taking into account that the sum of the angles of the triangle is 180 °:

Angle BAC = 180 ° – 90 ° – 60 ° = 30 °.

3. In a right-angled triangle ACH, the leg AH is located opposite an angle of 30 °, therefore, according to the properties of a right-angled triangle, its length is half the length of the hypotenuse AC:

AH = AC: 2 = 10: 2 = 5 cm.

Answer: the distance from vertex C to hypotenuse AB is 5 cm.