In a right-angled triangle ABC, angle C = 90, height CD = 12cm, AB = 25cm. Find AD

To solve this problem, we use the Pythagorean Theorem, which says:

c ^ 2 = a ^ 2 + b ^ 2, where a, b are legs, c is hypotenuse.

In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of its legs.

The two sides that make the angle ∠СDA straight are the legs.

In our task it is necessary to find one of these legs. The length of one (CD) is known and is 12 cm.

Substitute the known data into the formula and find the unknown value of AD:

25 ^ 2 = 12 ^ 2 + AD ^ 2

АD ^ 2 = 625 – 144

АD ^ 2 = 481

AD = 21

Answer: AD = 21 cm.