Question

Дано: треугольник прямоугольный abc, угол b - 45 градусам, угол a - 90 градусам, сторона bc - 20 см. найти: ba,ac. с объяснением и с решением!! ПО ТЕОРЕМЕ ПИФАГОРА​

Answer 1

Вс=20

ас=ав=x

по теореме Пифагора вс^2=ac^2+aв^2

вс=√ (х^2+x^2) = x√2

20=x√2

x=20/√2

x=10√2

ac=ав=10√2

Answer 2

Given Information:

We are given a right triangle ABC, where angle B is 45 degrees, angle A is 90 degrees, and side BC is 20 cm. We need to find the lengths of sides BA and AC using the Pythagorean theorem.

Solution:

According to the Pythagorean theorem, 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.

Let's denote the length of side BA as a and the length of side AC as b. The length of side BC is given as 20 cm.

Using the Pythagorean theorem, we have the following equation:

a^2 + b^2 = c^2

where c is the length of the hypotenuse, which is BC.

Since angle A is 90 degrees, we can use the Pythagorean theorem to find the lengths of sides BA and AC.

Calculation:

Using the Pythagorean theorem, we have:

a^2 + b^2 = c^2

Substituting the given values:

a^2 + b^2 = 20^2

Simplifying:

a^2 + b^2 = 400

Since angle B is 45 degrees, we can use the relationship between the sides of a 45-45-90 triangle. In a 45-45-90 triangle, the lengths of the two legs are equal, and the length of the hypotenuse is equal to the square root of 2 times the length of the legs.

Let's denote the length of side BA (which is equal to side AC) as x.

Using the relationship in a 45-45-90 triangle, we have:

x^2 + x^2 = 400

Simplifying:

2x^2 = 400

Dividing both sides by 2:

x^2 = 200

Taking the square root of both sides:

x = √200

Simplifying:

x = 10√2

Therefore, the lengths of sides BA and AC are both 10√2 cm.

Answer:

The length of side BA (which is equal to side AC) is 10√2 cm.