Question

Дан прямоугольный треугольник ABC, угол C - прямой. Найдите длину катета данного треугольника, если AB=5√2, и угол ABC=45° А) 555 В) 890 С) 345 D) нет верного ответа.

Answer 1

Надеюсь правильно
Т.к. угол авс равен 45град., то треугольник равнобедренный (180-90-45=45град).

В равнобедренном прямоугольном треугольнике катеты равны.

Квадрат гипотенузы равен сумме квадратов катетов, значит:
ав² = вс² + са²

(5√2)²=2*ас² (т.к. ас=св)
50=2*ас²
ас²=25
ас=св=5

Answer 2

Finding the Length of a Leg in a Right Triangle

To find the length of a leg in a right triangle, we can use the Pythagorean theorem. The Pythagorean theorem states that 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.

In this case, we are given a right triangle ABC, where angle C is a right angle. We are also given that AB = 5√2. We need to find the length of the leg of the triangle.

Let's denote the length of the leg as x. According to the Pythagorean theorem, we have:

x^2 + (5√2)^2 = AB^2

Simplifying the equation, we get:

x^2 + 50 = 50

Subtracting 50 from both sides, we have:

x^2 = 0

Taking the square root of both sides, we get:

x = 0

Therefore, the length of the leg of the given triangle is 0.

Please note that the given information and calculations result in a length of 0 for the leg of the triangle.