Question

В ПРЯМОУГОЛЬНОМ ТРЕУГОЛЬНИКЕ ОДИН ИЗ КАТЕТОВ РАВЕН 5 КОРНЕЙ ИЗ 3 СМНайдите гипотенузу если угол противолежащий данному катету равен 60 градуссов

Answer 1

Синус это отношение противолежащей стороны на гипотенузу, значит sin60=катет/гипотенузу. из этого следует что гипотенуза равна катет/синус. гипотенуза=5корень3/(корень3/2)=10. ответ 10

Answer 2

Finding the Hypotenuse of a Right Triangle

To find the hypotenuse of a right triangle when one of the legs is equal to 5√3 cm and the angle opposite to this leg is 60 degrees, we can use trigonometric functions.

Let's denote the hypotenuse as c, the leg equal to 5√3 cm as a, and the angle opposite to a as B.

Using the sine function, we can write:

sin(B) = a / c

Substituting the given values, we have:

sin(60 degrees) = 5√3 / c

To solve for c, we can rearrange the equation:

c = 5√3 / sin(60 degrees)

Now, let's calculate the value of c using this equation.

Calculation

Using the trigonometric identity sin(60 degrees) = √3 / 2, we can simplify the equation:

c = 5√3 / (√3 / 2)

Simplifying further:

c = 5√3 * (2 / √3)

c = 10 cm

Therefore, the length of the hypotenuse is 10 cm.

Conclusion

In a right triangle where one of the legs is equal to 5√3 cm and the angle opposite to this leg is 60 degrees, the length of the hypotenuse is 10 cm.