The height CO of a right-angled triangle is 9 cm and cuts off a segment AO equal to 12 cm

| September 3, 2021 | education

The height CO of a right-angled triangle is 9 cm and cuts off a segment AO equal to 12 cm from the hypotenuse AB Find AB and the sine of angle B.

Since triangle ABC is rectangular, and its height SB is drawn from the vertex of a right angle, then the square of its length is equal to the product of the segments into which SB divides AB.

CO2 = BO * AO.

BO = CO2 / AO = 81/12 = 27/4 = 6 (3/4) cm.

Then the length of the hypotenuse AB is equal to: AB = BO + AO = 6 (3/4) + 12 = (27 + 48) / 4 = 75/4 = 18.75 cm.

In a right-angled triangle BOS, according to the Pythagorean theorem, BC ^ 2 = BO ^ 2 + CO ^ 2 = (27/4) ^ 2 + 81 = (729 + 1296) / 16 = 2025/16.

BC = 45/4 cm.

SinСВО = СО / ВС = 9 / (45/4) = 36/45 = 4/5 = 0.8.

Answer: The length of the segment AB is 18.75 cm, SinCWO = 0.8.



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