Question

Гiпотенуза прямокутного триктника дорiвнюэ 20 см, один з кутiв 30°. Яка довжина меншого катета?

Answer 1

Против угла в 30 градусов лежит катит в 2 раза меньше гипотенузы, т,е, 10 см, второй катит равен 10$\sqrt{3}$. Значит меньший катит равен 10 см
 

Answer 2

Finding the Length of the Smaller Leg of a Right Triangle

To find the length of the smaller leg of a right triangle when the hypotenuse is 20 cm and one of the angles is 30°, we can use trigonometric functions to solve for the missing side.

Trigonometric Functions and Right Triangles

In a right triangle, the three main trigonometric functions are sine, cosine, and tangent. For a right triangle with angle θ, the functions are defined as follows: - Sine (sin θ): Opposite / Hypotenuse - Cosine (cos θ): Adjacent / Hypotenuse - Tangent (tan θ): Opposite / Adjacent

Calculating the Length of the Smaller Leg

Given that the hypotenuse is 20 cm and one of the angles is 30°, we can use the cosine function to find the length of the smaller leg.

Using the cosine function: cos(θ) = Adjacent / Hypotenuse

We can rearrange the formula to solve for the adjacent side: Adjacent = Hypotenuse * cos(θ)

Substituting the given values: Adjacent = 20 * cos(30°)

Calculation

Using the given cosine value from the search results: Adjacent = 20 * cos(30°) = 20 * 0.86602540378 ≈ 17.32 cm

So, the length of the smaller leg of the right triangle is approximately 17.32 cm.

This calculation is based on the trigonometric function for finding the length of the adjacent side of a right triangle when the hypotenuse and one angle are known