Question

Гіпотенуза прямокутного трикутника дорівнює 12 см.Знайдіть катет даного трикутника,проекція якого на гіпотенузу дорівнює 3 см.

Answer 1

Если проекция 3, то второй катет - 3.
12квадрат = 3 квадрат+ х квадрат
144 = 9 +125
корень из 125 ответ, если не имеется ввиду что нужно делать две проекции

Answer 2

Finding the Length of the Cathetus

To find the length of the cathetus (one of the sides) of a right triangle, given the length of the hypotenuse and the projection of the triangle on the hypotenuse, we can use the Pythagorean theorem.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

Let's denote the length of the hypotenuse as c and the projection on the hypotenuse as p. The length of the cathetus can be found using the following formula:

c^2 = a^2 + b^2

where a and b are the lengths of the catheti.

In this case, we are given that the length of the hypotenuse is 12 cm and the projection on the hypotenuse is 3 cm. Let's substitute these values into the formula:

12^2 = a^2 + 3^2

Simplifying the equation:

144 = a^2 + 9

Subtracting 9 from both sides:

135 = a^2

Taking the square root of both sides:

a = √135

Calculating the square root of 135:

a ≈ 11.62 cm

Therefore, the length of the cathetus of the given triangle is approximately 11.62 cm.