In a right-angled triangle ABC, the height CD is drawn from the vertex of the right angle, angle ABC = 56 degrees.

In a right-angled triangle ABC, the height CD is drawn from the vertex of the right angle, angle ABC = 56 degrees. Find the DCA angle.

The first way.

Since the segment CD is the height of the triangle ABC, then the triangle BCD is rectangular, then the angle BCD = (90 – ABC) = (90 – 56) = 34.

The angle ACB = 90, then the angle DCA = (90 – BCD) = (90 – 34) = 56.

Second way.

Triangles ABC and ACD are rectangular and similar in acute angle A, then the angle ABC and DCA are equal as similar angles of similar triangles. Angle DCA = ABC = 56.

Answer: The angle DCA is 56.