Question

Катеты прямоугольного треугольника соответственно равны 1 см и √3.Чему равна гипотенуза?

Answer 1

По теореме Пифагора:

с=√(1^2 + (√3)^2) = √(1+3) =√4 = 2

Answer 2

Solution:

Given that the lengths of the two legs (or catheti) of a right-angled triangle are 1 cm and √3 cm, we can use the Pythagorean theorem to find the length of the hypotenuse.

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 lengths of the other two sides.

So, for a right-angled triangle with legs of lengths a and b, and hypotenuse of length c, the theorem can be expressed as:

c^2 = a^2 + b^2

In this case, the lengths of the legs are 1 cm and √3 cm. Therefore, we can calculate the length of the hypotenuse as follows:

c^2 = (1 cm)^2 + (√3 cm)^2

c^2 = 1 cm^2 + 3 cm

c^2 = 1 + 3 cm^2

c^2 = 4 cm^2

Taking the square root of both sides, we get:

c = √4 cm

c = 2 cm

So, the length of the hypotenuse is 2 cm.

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