Question

у прямокутного трикутнику гіпотенуза дорівнює 30 см , а синус одного з кутів 0,6 . Знайдіть катети трикутника

Answer 1

Ответ:

18 см и 24 см

Объяснение:

Answer 2

Finding the lengths of the triangle's legs

To find the lengths of the legs of a right triangle, we can use the given information about the hypotenuse and the sine of one of the angles.

Let's denote the lengths of the legs of the triangle as a and b, and the length of the hypotenuse as c.

Given: - Hypotenuse (c) = 30 cm - Sine of one of the angles (sin(θ)) = 0.6

We can use the following formulas to find the lengths of the legs:

1. Using the Pythagorean theorem: c^2 = a^2 + b^2. 2. Using the sine function: sin(θ) = a/c.

Let's solve for a and b using these formulas.

Using the Pythagorean theorem: c^2 = a^2 + b^2 Substituting the given values: 30^2 = a^2 + b^2 Simplifying: 900 = a^2 + b^2 (Equation 1)

Using the sine function: sin(θ) = a/c Substituting the given values: 0.6 = a/30 Simplifying: a = 0.6 * 30 a = 18 (Equation 2)

Now, we can substitute the value of a from Equation 2 into Equation 1 to solve for b.

900 = 18^2 + b^2 900 = 324 + b^2 b^2 = 900 - 324 b^2 = 576 b = √576 b = 24

Therefore, the lengths of the legs of the triangle are: a = 18 cm b = 24 cm