In triangle ABC, angle C is 90 degrees, Bc = 8, AC = 6. Find the cosine of angle A.

A triangle is three points that do not lie on one straight line, connected by segments. In this case, the points are called the vertices of the triangle, and the segments are called its sides.

If in a triangle one of the angles is straight (equal to 90º), then this triangle is right-angled. 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 calculate the cosine of angle A, you must first find the length of the hypotenuse AB. To do this, we use the Pythagorean theorem, according to which the square of the hypotenuse is equal to the sum of the squares of the legs:

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

AB ^ 2 = 8 ^ 2 + 6 ^ 2 = 64 + 36 = 100;

AB = √100 = 10 cm.

cos A = 6/10 = 0.6.

Answer: The cosine of angle A is 0.6.