# In the triangle ABC It is known that the angle C = 90 °, the angle B = 30 °, on the leg BC we marked

March 28, 2021 | education

| **In the triangle ABC It is known that the angle C = 90 °, the angle B = 30 °, on the leg BC we marked the point D such that the angle ADC = 60 °. Find the leg BC if CD = 5 cm.**

In a right-angled triangle ABC, the second acute angle CAB is equal to:

∠ САВ = 90 ° – ∠ В = 90 ° – 30 ° = 60 °.

In a right-angled triangle ACD, the second acute angle CAD is:

∠ CAD = 90 ° – ∠ CDA = 90 ° – 60 ° = 30 °.

Leg CD = 5 cm and lies opposite this corner. It follows from this that the hypotenuse AD = 2 * 5 = 10 (cm).

Consider triangle ADB, in it:

∠ B = 30 °,

∠ DAB = ∠ CAB – ∠ CAD = 60 ° – 30 ° = 30 °.

We get that triangle ADB is isosceles, AD = BD = 10 (cm).

BC = CD + BD = 5 + 10 = 15 (cm).

Answer: the BC leg is 15 cm.

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