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 20cm, the length of the BC side is 15cm. Find NC.

1. In right-angled triangle ABN, leg BN is opposite to angle BAN, side AB of this triangle is the hypotenuse. Their ratio is the sine of the angle BAN.

2. We calculate the height BN of the triangle ABC:

BN / AB = 0.6;

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

3. The segment СN is the leg of the right-angled triangle BCN, the side of this triangle BC is the hypotenuse.

4. Applying the Pythagorean theorem, we calculate the length of the leg СN:

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

Answer: CN length is 9 cm.