Question

Гіпотенуза прямокутного трикутника = 15 см, синус кута А = 4/5. Знайти катети.

Answer 1

Ответ:

первый катет: 15/1=х/0.8. х=(0.8*15):1=9

второй катет: √225-81=√144=12

Объяснение:

чтобы найти первый катет было использована теорема синусов, а на втором теорема Пифагора.

удачки:)

Answer 2

Finding the Length of the Hypotenuse

To find the length of the hypotenuse of a right triangle, we can use the Pythagorean theorem, which 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 lengths of the other two sides (the legs) as a and b. According to the Pythagorean theorem, we have the equation:

c^2 = a^2 + b^2

In this case, we are given that the length of the hypotenuse is 15 cm. So we have:

15^2 = a^2 + b^2

Simplifying this equation, we get:

225 = a^2 + b^2

Finding the Length of the Legs

To find the lengths of the legs of the right triangle, we need additional information. In this case, we are given the sine of angle A, which is equal to 4/5. The sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse.

Let's denote the length of the side opposite angle A as a and the length of the hypotenuse as c. According to the definition of sine, we have the equation:

sin(A) = a / c

Substituting the given values, we get:

4/5 = a / 15

To find the length of side a, we can solve this equation:

a = (4/5) * 15 = 12 cm Now, to find the length of side b, we can use the Pythagorean theorem equation we derived earlier:

225 = a^2 + b^2

Substituting the known value of a:

225 = 12^2 + b^2

Simplifying this equation, we get:

225 = 144 + b^2

Subtracting 144 from both sides:

81 = b^2

Taking the square root of both sides:

b = √81 = 9 cm

So, the lengths of the legs of the right triangle are a = 12 cm and b = 9 cm.