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

June 27, 2021 | education

| **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.

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