Question

В прямоугольном треугольнике РКТ(угол Т – прямой) КТ=7см, РТ=7см. Найдите угол К и гипотенузу КР.

Answer 1

Т. к. катеты равны, то прямоугольный треугольник является равнобедренным, а в равнобедренном треугольнике углы при основании ( она же и гипотенуза)
180°-90°=90°
<К=<Р=45°
по теореме Пифагора
КТ²+РТ²=КР²
КР=√7²+7²=√49+49=√98=9,89

Answer 2

Finding the Angle K and Hypotenuse KR in a Right Triangle

To find the angle K and the hypotenuse KR in a right triangle RKT, where angle T is a right angle, KT is 7 cm, and RT is 7 cm, we can use the properties of right triangles.

Let's start by finding the angle K. In a right triangle, the sum of the angles is always 180 degrees. Since angle T is a right angle (90 degrees), the sum of angles RKT and KRT must be 90 degrees as well. Therefore, angle K is equal to 180 degrees minus the sum of angles RKT and KRT.

To find the hypotenuse KR, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, the hypotenuse KR is the side opposite the right angle T, and the other two sides are KT and RT.

Now let's calculate the angle K and the hypotenuse KR.

Calculating the Angle K

The angle K can be found by subtracting the sum of angles RKT and KRT from 180 degrees. Since angle T is a right angle (90 degrees), the sum of angles RKT and KRT is also 90 degrees. Therefore, angle K is equal to 180 degrees minus 90 degrees.

Angle K = 180° - 90° = 90°

Calculating the Hypotenuse KR

The Pythagorean theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, the hypotenuse KR is the side opposite the right angle T, and the other two sides are KT and RT.

Using the given information, we have KT = 7 cm and RT = 7 cm. Let's substitute these values into the Pythagorean theorem equation and solve for KR.

KR^2 = KT^2 + RT^2 KR^2 = 7^2 + 7^2 KR^2 = 49 + 49 KR^2 = 98 KR = √98

Therefore, the hypotenuse KR is equal to the square root of 98.

Hypotenuse KR = √98 cm

To summarize: - Angle K is equal to 90 degrees. - The hypotenuse KR is equal to the square root of 98 cm.

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