Question

В треугольнике АВС угол С равен 90 градусов,АВ=30,АС=24.Найти тангес А

Answer 1

CB^2 = AB^2 - CA^2 = 324 ( по теореме пифогора )

CB = 18

тангес - отношения противолежащего катета к прилежащему

tgA = CB \ AC = 3\4

 

Answer 2

Given Information

We are given the following information about triangle ABC: - Angle C is equal to 90 degrees. - Side AB has a length of 30. - Side AC has a length of 24.

Finding the Tangent of Angle A

To find the tangent of angle A, we can use the formula tg(A) = BC/AC. However, we need to find the length of side BC first.

To find the length of side BC, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Using the Pythagorean theorem, we can write the equation AB^2 = BC^2 + AC^2.

Substituting the given values, we have 30^2 = BC^2 + 24^2.

Simplifying the equation, we get 900 = BC^2 + 576.

Rearranging the equation, we have BC^2 = 900 - 576.

Simplifying further, we get BC^2 = 324.

Taking the square root of both sides, we find BC = 18.

Now that we know the length of side BC, we can find the tangent of angle A using the formula tg(A) = BC/AC.

Substituting the values, we have tg(A) = 18/24.

Simplifying the expression, we find tg(A) = 0.75.

Therefore, the tangent of angle A is 0.75.

Answer

The tangent of angle A in triangle ABC is 0.75.