Question

У прямокутному трикутнику гипотенуза и катет мы должны 25 см и 12,5см знайдить кути трикутника​

Answer 1

Ответ:

90°;60°;30°

Объяснение:

ВC=25см

ВА=12,5

ВС=2*ВА; катет ВА лежить проти кута 30°;

∠С=30°

Сума гострих кутів прямокутного трикутника дорівнює 90°

∠В=90°-∠С=90°-30°=60°

∠ВАС=90°, трикутник прямокутний.

Answer 2

Finding the angles of a right triangle

To find the angles of a right triangle, we can use trigonometric functions such as sine, cosine, and tangent. In this case, we are given the lengths of the hypotenuse and one of the legs of the triangle, and we need to find the angles.

Let's denote the hypotenuse as c and the legs as a and b. In this case, c is given as 25 cm and one of the legs, a, is given as 12.5 cm.

To find the angles, we can use the following trigonometric ratios:

1. Sine: sin(angle) = opposite/hypotenuse 2. Cosine: cos(angle) = adjacent/hypotenuse 3. Tangent: tan(angle) = opposite/adjacent

In this case, we can use the sine function to find one of the angles. Since we are given the length of the hypotenuse and one of the legs, we can use the sine function as follows:

sin(angle) = opposite/hypotenuse

sin(angle) = a/c

sin(angle) = 12.5/25

sin(angle) = 0.5

To find the angle, we can take the inverse sine (also known as arcsine) of 0.5. This can be done using a scientific calculator or an online calculator. The inverse sine of 0.5 is approximately 30 degrees.

Therefore, one of the angles of the right triangle is approximately 30 degrees.

To find the other angle, we can use the fact that the sum of the angles in a triangle is 180 degrees. Since we already know one angle (30 degrees), we can subtract it from 180 to find the other angle:

Other angle = 180 - 30 = 150 degrees

Therefore, the other angle of the right triangle is 150 degrees.

In summary, the angles of the given right triangle with a hypotenuse of 25 cm and a leg of 12.5 cm are approximately 30 degrees and 150 degrees.

Please note that the calculations provided are based on the information given in the question.