Question

В прямоугольном треугольнике abc угол с 90 градусов угол а 45 градусов, а гипотинуза равна 10 см. Найти катеты abc.

Answer 1

Оба катета равны 5. (а^2+a^2)^2=10
2a^2=10
a^2=5
a=$\sqrt{5}$

Answer 2

Given Information

We are given a right triangle ABC, where angle C is 90 degrees, angle A is 45 degrees, and the hypotenuse is 10 cm. We need to find the lengths of the other two sides (the legs) of the triangle.

Solution

To find the lengths of the legs of the triangle, we can use trigonometric ratios. In this case, we can use the sine and cosine ratios.

Let's denote the length of side AB as a, the length of side BC as b, and the length of side AC (the hypotenuse) as c.

Using the given information, we have: - Angle A = 45 degrees - Angle C = 90 degrees - Hypotenuse AC = 10 cm

We can use the sine ratio to find the length of side AB: sin(A) = AB/AC sin(45) = a/10

We can use the cosine ratio to find the length of side BC: cos(A) = BC/AC cos(45) = b/10

Now, let's calculate the values of a and b using these equations.

Calculation

Using the sine ratio: sin(45) = a/10 Simplifying the equation: a = 10 * sin(45)

Using the cosine ratio: cos(45) = b/10 Simplifying the equation: b = 10 * cos(45)

Now, let's calculate the values of a and b.

Calculation

Using a calculator, we can find the values of sin(45) and cos(45): sin(45) ≈ 0.7071 cos(45) ≈ 0.7071

Substituting these values into the equations: a = 10 * 0.7071 ≈ 7.071 cm b = 10 * 0.7071 ≈ 7.071 cm

Therefore, the lengths of the legs of the triangle ABC are approximately 7.071 cm each.

Answer

The lengths of the legs of the triangle ABC are approximately 7.071 cm each.