# From the vertex of the right angle of the right-angled triangle ABC, the height CD is drawn.

August 30, 2021 | education

| **From the vertex of the right angle of the right-angled triangle ABC, the height CD is drawn. Find the angle BCD. If 1) angle A = 25; 2) angle A = 70 degrees**

Since a given triangle ABC is rectangular, the height CD, lowered from its right angle ACB, divides triangle ABC into two similar right-angled triangles BDC and ADC with equal angles BCD = CAD (∠ACD = 180 ° – ∠ADC – ∠САD = 90 ° – САD; ∠ВDC = ∠АСВ – ∠АСD = 90 ° – ∠АСD = 90 ° – (90 ° – ∠САD) = ∠САD) and DVS = DCA similarly.

So if

1) the specified angle A (∠САD) is 25 °, then ∠BCD = 25 °;

2) the given angle A (∠САD) is 70 °, then ∠BCD = 70 °.

Answer: 1) ∠BCD = 25 °; 2) ∠BCD = 70 °.

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