Question

Abc прмоугольный треугольник угол C=90 градусов tgA=0.25 Ac=10 найти AB и BC​

Answer 1

Ответ на картинке…..

Answer 2

Problem Analysis

We are given a right triangle ABC, where angle C is 90 degrees. We are also given that the tangent of angle A is 0.25 and the length of side AC is 10. We need to find the lengths of sides AB and BC.

Solution

To solve this problem, we can use the trigonometric ratios of a right triangle. In particular, we can use the tangent ratio to find the lengths of the sides.

The tangent of an angle in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. In this case, we are given that the tangent of angle A is 0.25, so we can write:

tan(A) = AB / BC

We are also given that the length of side AC is 10, so we can write:

AC = AB + BC

We can use these two equations to solve for the lengths of sides AB and BC.

Solution Steps

1. Substitute the given values into the equation tan(A) = AB / BC: 0.25 = AB / BC

2. Rearrange the equation to solve for AB: AB = 0.25 * BC

3. Substitute the value of AB into the equation AC = AB + BC: 10 = 0.25 * BC + BC

4. Simplify the equation: 10 = 1.25 * BC

5. Solve for BC: BC = 10 / 1.25 = 8

6. Substitute the value of BC into the equation AB = 0.25 * BC: AB = 0.25 * 8 = 2

Therefore, the length of side AB is 2 and the length of side BC is 8.

Answer

The length of side AB is 2 and the length of side BC is 8.