In a right-angled triangle ABC, the height BH, drawn from the top of the right angle B, divides the hypotenuse

| July 6, 2021 | education

In a right-angled triangle ABC, the height BH, drawn from the top of the right angle B, divides the hypotenuse into two segments AH = 36cm and CH = 25cm. Find: a) BH, AB, BC b) SАВН: SСВН

Since the height BH is lowered to the hypotenuse from the vertex of the right angle, its length will be equal to:

BH = √ (AH * BH) = √36 * 25 = √900.

BH = 30 cm.

From the right-angled triangle ABH we determine the length of the hypotenuse AB.

AB ^ 2 = AH ^ 2 + BH ^ 2 = 1296 + 900 = 2196.

AB = 6 * √61 cm.

From the right-angled triangle BСН we determine the length of the hypotenuse BC.

BC ^ 2 = CH ^ 2 + BH ^ 2 = 625 + 900 = 1525.

BC = 5 * √61 cm.

Determine the area of the triangle ABH. Savn = AH * BH / 2 = 36 * 30/2 = 540 cm2.

Determine the area of the BCH triangle. Svsn = CH * BH / 2 = 25 * 30/2 = 375 cm2.

Answer: BH = 30 cm, AB = 6 * √61 cm, BC = 5 * √61 cm, Sav = 540 cm2, Svsn = 375 cm2.



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.