In a right-angled triangle ABC, angle C = 90 degrees, AB = √13, AC = 3, find the ctg of angle A

Given: ABC – rectangle. treug .;

C = 90 °;

AB = √ (13), AC = 3;

ctg А -? °

Because ABC is rectangular. treug., it means that ratios and dependencies between angles and sides work for him.

By the Pythagorean theorem, we calculate the length of the BC leg:

ВС = √ (AB ^ 2 – AC ^ 2) = √ (13 – 9) = 2.

Angle A is acute, let’s find the catangent of this angle. In rectangular. treug. the catangent of an acute angle is the ratio of the legs of the triugs adjacent to this angle. to the opposite.

ctg A = AC / BC = 3/2 = 1.5.

Answer: the catangent of angle A is 1.5.