The height BN is drawn in an acute-angled triangle ABC. The sine of the angle BAC is 0.6.

The height BN is drawn in an acute-angled triangle ABC. The sine of the angle BAC is 0.6. The length of the AB side is 20 cm, the length of the BC side is 15 cm. Find NC.

1. In a right-angled triangle ABN, the height BN is the leg opposite the angle BAC, the sine of which is 0.6. Based on the fact that the quotient of dividing the length of this leg by the length of the hypotenuse AB is the sine of the angle BAC, we calculate the length BN:

BN: AB = 0.6.

BN = 0.6 x AB = 0.6 x 20 = 12 centimeters.

2. We calculate the length of the segment СN using the formula of the Pythagorean theorem:

CN = √BC ^ 2 – BN ^ 2 = √15 ^ 2 – 12 ^ 2 = √81 = 9 centimeters.

Answer: the length of the segment СN is 9 centimeters.