Question

В треугольнике АВС угол С= 90 градусовАС = 12тангенс А = 0,5Найти ВС ПОМОГИТЕ, ПОЖАЛУЙСТА

Answer 1

TgA = BC/AC
ВС = АС * tgA
BC = 12 * 0,5 = 6

Answer 2

Problem Analysis

We are given a triangle ABC, where angle C is 90 degrees, AC is 12, and the tangent of angle A is 0.5. We need to find the length of side BC.

Solution

To find the length of side BC, we can use the tangent function and the Pythagorean theorem.

Let's start by finding the length of side AB. We know that the tangent of angle A is equal to the ratio of the length of side AB to the length of side BC. Therefore, we can write:

tan(A) = AB / BC

Given that the tangent of angle A is 0.5, we can substitute this value into the equation:

0.5 = AB / BC

Next, we can use the Pythagorean theorem to relate the lengths of sides AB, BC, and AC. The Pythagorean theorem 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. In our case, we have:

AB^2 + BC^2 = AC^2

Substituting the known values, we get:

AB^2 + BC^2 = 12^2

Simplifying further, we have:

AB^2 + BC^2 = 144

Now, we can solve these two equations simultaneously to find the lengths of sides AB and BC.

Calculation

Let's solve the equations:

Equation 1: 0.5 = AB / BC

Equation 2: AB^2 + BC^2 = 144

From Equation 1, we can rewrite it as:

AB = 0.5 * BC

Substituting this into Equation 2, we get:

(0.5 * BC)^2 + BC^2 = 144

Simplifying further:

0.25 * BC^2 + BC^2 = 144

Combining like terms:

1.25 * BC^2 = 144

Dividing both sides by 1.25:

BC^2 = 144 / 1.25

Taking the square root of both sides:

BC = sqrt(144 / 1.25)

Evaluating the square root:

BC ≈ 10.909

Therefore, the length of side BC is approximately 10.909.

Answer

The length of side BC in triangle ABC is approximately 10.909.