Question

В Треугольнике ABC угол С равен 90 градусов AB=6, tgA= 2√2Найдите AC Если можно то с подробным объяснением ) Заранее спасибо

Answer 1

Если <C прямой, тогда АВ -- гипотенуза этого прямоугольного треугольника;
ВС -- противолежащий, а АС -- прилежащий катет (относительно <A).
По определению, tg<A = BC/AC, т. е. BC/AC = 2√2 или BC = 2√2·AC.
Примем АС = х. Тогда ВС = 2√2·х.
По теореме Пифагора: АВ² = АС² + ВС².
6² = х² + (2√2·х)²
36 = х² + 8х²
36 = 9х²
х² = 4
х = +-2
Поскольку х -- это длина отрезка, она не может быть отрицательной.
Тогда, окончательно: АС = 2

Answer 2

Given Information

We are given the following information about triangle ABC: - Angle C is 90 degrees. - AB = 6. - tg(A) = 2√2.

Solution

To find AC, we can use the trigonometric relationship between the sides and angles of a right triangle. In this case, we can use the tangent function.

The tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side. In triangle ABC, angle A is the angle opposite side AC, and side AB is the adjacent side.

We are given that tg(A) = 2√2. This means that the length of the opposite side (AC) divided by the length of the adjacent side (AB) is equal to 2√2.

Using this information, we can set up the following equation:

tg(A) = AC / AB

Substituting the given values:

2√2 = AC / 6

To solve for AC, we can cross-multiply:

AC = 6 * 2√2

Simplifying:

AC = 12√2

Therefore, the length of AC is 12√2.

Summary

In triangle ABC, with angle C equal to 90 degrees, AB equal to 6, and tg(A) equal to 2√2, the length of AC is 12√2.