In triangle ABC, angle C is 90 degrees, AB = 25, BC = 24, find cosA

A triangle that contains an angle of 90º is rectangular. The side opposite to the right angle is called the hypotenuse, and the other two are called the legs.

The cosine of an acute angle of a right-angled triangle is the ratio of the adjacent leg to the hypotenuse:

cos A = AC / AB.

To do this, you need to calculate the length of the AC leg. Let’s apply the Pythagorean theorem:

AB ^ 2 = BC ^ 2 + AC ^ 2;

AC ^ 2 = AB ^ 2 – BC ^ 2;

AC ^ 2 = 25 ^ 2 – 24 ^ 2 = 625 – 576 = 49;

AC = √49 = 7 cm.

cos A = 7/25 = 0.28.

Answer: The cosine of angle A is 0.28.




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