In a right-angled triangle ABC, the height BD is 24 cm and cuts off the DC segment equal to 18 cm

In a right-angled triangle ABC, the height BD is 24 cm and cuts off the DC segment equal to 18 cm from the hypotenuse AC.Find AB and cosA

1. Using the formula for calculating the height, drawn from the vertex of the right angle to the hypotenuse, we calculate the length of the segment AD:

ВD = √АD x СD;

BD ^ 2 = AD x CD;

AD = BD ^ 2 / CD = 24 ^ 2/18 = 576/18 = 32 cm.

2. Applying the Pythagorean theorem, we calculate the length of the hypotenuse AB:

AB = √BD ^ 2 + AD ^ 2 = √32 ^ 2 + 24 ^ 2 = √1024 + 576 = √1600 = 40 cm.

3. We calculate the value of cosA, which is equal to the ratio of the adjacent leg AD to the hypotenuse AB:

cosA = AD / AB = 32/40 = 0.8;

Answer: The length of the hypotenuse AB is 40 cm, cosA is 0.8.