Question

В ТРЕУГОЛЬНИКЕ АВС угол С равен 90 градусов .АВ =20 АС = 16 .найдите tga

Answer 1

По т.Пифагора
ВС²=АВ²-АС²=20²-12²=256
ВС=16
tg α = ВС:АС=16:12=4/3

Answer 2

Given Information

We are given a triangle ABC, where angle C is 90 degrees, AB is 20, and AC is 16. We need to find the value of tga.

Solution

To find the value of tga, we can use the tangent function, which is defined as the ratio of the length of the opposite side to the length of the adjacent side in a right triangle.

In this case, angle A is the acute angle opposite side AC, and side AB is the adjacent side. Therefore, we can use the formula tg(A) = BC/AC, where BC is the length of the side opposite angle B.

To find the length of 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 find the length of BC as follows:

BC^2 = AB^2 - AC^2 BC^2 = 20^2 - 16^2 BC^2 = 400 - 256 BC^2 = 144 BC = √144 BC = 12

Now that we have the lengths of BC and AC, we can find the value of tg(A) as follows:

tg(A) = BC/AC tg(A) = 12/16 tg(A) = 0.75

Therefore, the value of tga is 0.75.

Answer

The value of tga in the given triangle ABC, where angle C is 90 degrees, AB is 20, and AC is 16, is 0.75.