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 DCA angle if the angle B = 36 degrees.

1. Let us introduce the designation of the angle by the symbol ∠.

2. Triangle BCD is rectangular, since the height of CD forms 90 ° with side AB ∠BDC.

3. We calculate the value of ∠ВCD, taking into account that the total value of all angles of any triangle is 180 °:

∠ВCD = 180 ° – ∠DВC – ∠ВDC = 180 ° – 36 ° – 90 ° = 54 °.

4. Calculate the value of the sought ∠ВCА:

∠ВCА = ∠АСВ – ∠ВCD = 90 ° – 54 ° = 36 °

Answer: ∠BCA is equal to 36 °.