Question

Помогите пожалуйста. У прямоугольного треугольника один катет равен 8см, а синус противолежащего ему угла равен 0,8. Найдите гипотенузу и второй катет. можно полное решение .

Answer 1

Синус-это отношение противолежащего катета к гипотенузе надеюсь понятно решение)

Answer 2

Problem Analysis

We are given a right triangle with one leg measuring 8 cm and the sine of the angle opposite to that leg equal to 0.8. We need to find the length of the hypotenuse and the length of the other leg.

Solution

Let's denote the length of the hypotenuse as c, the length of the leg adjacent to the given angle as a, and the length of the leg opposite to the given angle as b.

We are given that a = 8 cm and sin(θ) = 0.8, where θ is the angle opposite to the leg of length 8 cm.

Using the definition of sine, we have:

sin(θ) = b / c

Rearranging the equation, we get:

b = sin(θ) * c

Substituting the given values, we have:

8 = 0.8 * c

Simplifying the equation, we find:

c = 8 / 0.8 = 10 cm

So, the length of the hypotenuse is 10 cm.

To find the length of the other leg, 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.

Applying the Pythagorean theorem, we have:

a^2 + b^2 = c^2

Substituting the known values, we get:

8^2 + b^2 = 10^2

Simplifying the equation, we find:

64 + b^2 = 100

Subtracting 64 from both sides, we have:

b^2 = 36

Taking the square root of both sides, we find:

b = 6 cm

So, the length of the other leg is 6 cm.

Therefore, the length of the hypotenuse is 10 cm and the length of the other leg is 6 cm.

Conclusion

In a right triangle with one leg measuring 8 cm and the sine of the angle opposite to that leg equal to 0.8, the length of the hypotenuse is 10 cm and the length of the other leg is 6 cm.