In a right-angled triangle ABC, the height CD is drawn from the vertex of the right angle C.

In a right-angled triangle ABC, the height CD is drawn from the vertex of the right angle C. Find the angle BCD if angle A is 60 degrees.

Since in a right-angled triangle ABC, angle A = 60 °, and angle C = 90 °, we get that angle B = 180 ° – 90 ° – 60 ° = 30 °.

Since we know that the height is drawn from the right angle C to the hypotenuse AB, it turns out that the angle CDB is a straight line = 90 °.

Consider a right-angled triangle CDB in which we know two angles:

angle CDB – straight line = 90 °;

angle DBC = angle B = 30 °;

Thus, knowing that the sum of all the angles of the triangle is 180 °, we get that:

angle BCD = 180 ° – angle CDB – angle DBC = 180 ° – 90 ° – 30 ° = 60 °.

Answer: 60 °.