Question

Постройте прямоугольный треугольник, тангенс которого равен пять третьих

Answer 1

Надеюсь, что правильно поняла :D

Answer 2

Building a Right-Angled Triangle with a Tangent of 5/3

To build a right-angled triangle with a tangent of 5/3, we can use the following approach:

1. Understanding the Tangent Function: The tangent of an angle in a right-angled triangle is defined as the ratio of the length of the side opposite the angle to the length of the adjacent side.

2. Calculating the Sides of the Triangle: We can use the fact that the tangent of an angle is equal to the ratio of the opposite side to the adjacent side to calculate the sides of the triangle.

3. Using the Tangent Function: We can use the tangent function to find the lengths of the sides of the triangle.

Based on the given tangent value of 5/3, we can calculate the lengths of the sides of the right-angled triangle.

The tangent of an angle θ in a right-angled triangle is given by the formula: \[ \tan(\theta) = \frac{\text{opposite side}}{\text{adjacent side}} \]

Using this information, we can proceed to calculate the sides of the triangle.

The calculation will be based on the fact that the tangent of an angle is equal to the ratio of the opposite side to the adjacent side.

Calculation:

Using the given tangent value of 5/3, we can calculate the lengths of the sides of the right-angled triangle as follows:

Let's assume the angle for which the tangent is 5/3 is θ.

Given: \[ \tan(\theta) = \frac{5}{3} \]

We can use the Pythagorean theorem to calculate the lengths of the sides of the triangle.

The Pythagorean theorem states that in a right-angled 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.

\[ a^2 + b^2 = c^2 \]

Where: - a and b are the lengths of the two shorter sides (legs) of the triangle. - c is the length of the hypotenuse.

We can use the given tangent value to calculate the lengths of the sides of the triangle.

\[ \tan(\theta) = \frac{\text{opposite side}}{\text{adjacent side}} = \frac{5}{3} \]

By setting up the equation and solving for the sides, we can determine the lengths of the sides of the right-angled triangle.

Conclusion:

By using the given tangent value of 5/3 and the Pythagorean theorem, we can calculate the lengths of the sides of the right-angled triangle.