The height CH is drawn in triangle ABC with hypotenuse AB equal to 18 cm. Find BH and HA if angle A = 30 degrees.

CB – a leg, lying opposite an angle of 30 °, which means CB = 1/2 AB = 1/2 * 18 = 9 (cm);

AC² = AB² – CB²;

AC² = 324 – 81 = 243 (cm²); AC = √243 cm;

From the triangle ACH CH = 1/2 AC = 1/2 √243 (cm);

AH² = AC² – CH²;

AH² = 243 – 1/4 * 243; AH² = 3/4 * 243 = 729/4 (cm²);

AH = √ (729/4) = 27/2 = 13.5 (cm);

HB = AB – AH;

HB = 18 – 13.5 = 14.5 (cm).

Answer: BH = 14.5 cm; HA = 13.5 cm.