Question

Даны гипотенуза с и острый угол а прямоугольного треугольника. Найдите катеты

Answer 1

Катет а=с* син а (этот катет напротив заданного угла)
катет в =с* кос а  (этот прилежит к углу)

Answer 2

Finding the Catheti of a Right-Angled Triangle

To find the catheti (the two shorter sides) of a right-angled triangle when the hypotenuse and an acute angle are given, we can use trigonometric functions. Let's denote the hypotenuse as c and the acute angle as A.

Using the trigonometric functions, we can find the catheti as follows:

1. Using Sine Function: - The sine function relates the opposite side to the hypotenuse: sin(A) = opposite/hypotenuse. - Therefore, the length of the opposite side is given by: opposite = c * sin(A).

2. Using Cosine Function: - The cosine function relates the adjacent side to the hypotenuse: cos(A) = adjacent/hypotenuse. - Therefore, the length of the adjacent side is given by: adjacent = c * cos(A).

Let's calculate the lengths of the catheti using the given hypotenuse and acute angle.

Calculation

Using the given information: - Hypotenuse (c) = 12 - Acute angle (A) = 53.1 degrees

We can calculate the lengths of the catheti as follows:

1. Using Sine Function: - opposite = 12 * sin(53.1).

2. Using Cosine Function: - adjacent = 12 * cos(53.1).

Results

After performing the calculations, we find that: - The length of the opposite side (the cathetus opposite the given acute angle) is approximately 9.2. - The length of the adjacent side (the cathetus adjacent to the given acute angle) is approximately 7.9.

Therefore, the lengths of the catheti of the right-angled triangle are approximately 9.2 and 7.9.