In triangle ABC, angle C is 90 °, BC = 6, ctgA = 0.75. Find AB.

In triangle ABC, we find the hypotenuse AB, if it is known:

Angle C = 90 °;
BC = 6;
ctg A = 0.75.
Decision:

1) First, find the second leg of the AC.

The cotangent of the angle is equal to the ratio of the adjacent leg to the opposite leg. That is, we get the formula:

ctg a = AC / BC;

From here we find the AC.

AC = BC * ctg a;

Substitute the known values into the formula and calculate the second leg of the AC.

AC = 6 * 0.75 = 6 * 3/4 = 6/4 * 3 = 3/2 * 3 = 9/2;

2) Find the hypotenuse AB by the Pythagorean theorem:

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

AB ^ 2 = (9/2) ^ 2 + 6 ^ 2 = 20.25 + 36 = 56.25 = 7.5 ^ 2;

AB = 7.5.