Question

В треугольнике ABC угол C равен 90°, BC=2, sinA=0.4. Найти AB.

Answer 1

Sin α = CB/AB ⇒ AB = CB/ sin α = 2/ 0,4 = 5
Ответ: 5

Answer 2

Given that in triangle ABC, angle C is 90°, BC = 2, and sin A = 0.4, we need to find the length of AB.

To find AB, we can use the Pythagorean theorem and trigonometric ratios.

Pythagorean theorem:

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 other two sides.

In this case, AB is the hypotenuse, and BC and AC are the other two sides. So we can write:

AB^2 = BC^2 + AC^2

Trigonometric ratio:

We are also given that sin A = 0.4. The sine of an angle in a right-angled triangle is defined as the ratio of the length of the side opposite that angle to the length of the hypotenuse.

In this case, sin A = AC / AB. So we can write:

AC = sin A * AB

Now we can substitute the value of AC in the Pythagorean theorem equation:

AB^2 = BC^2 + (sin A * AB)^2

Simplifying the equation:

AB^2 = 2^2 + (0.4 * AB)^2 AB^2 = 4 + 0.16 * AB^2 AB^2 - 0.16 * AB^2 = 4 0.84 * AB^2 = 4 AB^2 = 4 / 0.84 AB^2 = 4.76

Taking the square root of both sides:

AB = sqrt(4.76) AB ≈ 2.18

Therefore, the length of AB is approximately 2.18 units.