Question

В треугольнике мрк, угол р=90 градусов, мр=10 см, высота ро=6 см. Найти катет РКИ косинус к

Answer 1

Треугольник РОМ
ОМ^2=10^2-6^2=64  ОМ=8
РО^2=КО*ОМ  36=КО*8 КО=4,5
КМ=ОМ+КО=8+4,5=12,5
КР^2=KM^2-PM^2=12,25^2-10^2=56,25  KP=7,5
cos K=КР/КМ=7,5/12,5=0,6

Answer 2

Given Information:

We are given the following information about a right-angled triangle MRK: - Angle R is 90 degrees. - Side MR is 10 cm. - Height RO is 6 cm.

Finding the Length of Side RKI:

To find the length of side RKI, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, side RKI is the hypotenuse, and sides MR and RO are the other two sides. Therefore, we can write the equation as:

RKI^2 = MR^2 + RO^2

Substituting the given values, we have:

RKI^2 = 10^2 + 6^2 RKI^2 = 100 + 36 RKI^2 = 136

Taking the square root of both sides, we find:

RKI = √136 RKI ≈ 11.66 cm

Therefore, the length of side RKI is approximately 11.66 cm.

Finding the Cosine of Angle K:

To find the cosine of angle K, we can use the definition of cosine in a right-angled triangle. The cosine of an angle is equal to the ratio of the length of the adjacent side to the hypotenuse.

In this case, angle K is the acute angle opposite side RKI, and side MR is the adjacent side. Therefore, we can write the equation as:

cos(K) = MR / RKI

Substituting the given values, we have:

cos(K) = 10 / 11.66 cos(K) ≈ 0.858

Therefore, the cosine of angle K is approximately 0.858.