Question

1. Найдите синус, косинус и тангенс острых углов прямоугольного треугольника с катетами 7 см и 15 см. Помогите пожалуйста НАДО ДАНО НАЙТИ РЕШИТЕ ОТВЕТ ​

Answer 1

пусть дан треугольник АВС, ∠С=90°,  АС=7см; ВС=15 см,

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Найти sin∠А; sin∠В; cos∠А; cos∠В

Решение

 АВ =√(АС²+ВС²)=

√(49+225)=√274;

sin∠А=ВС/АВ=15/√274;

sin∠В=АС/АВ=15/√274;

cos∠А=АС/АВ=7/√274;

cos∠В=ВС/АВ=15/√274

ОТВЕТ

sin∠А=15/√274;

sin∠В=15/√274;

cos∠А=7/√274;

cos∠В=15/√274

Answer 2

Finding the Trigonometric Ratios of an Acute Angle in a Right Triangle

To find the sine, cosine, and tangent of the acute angles in a right triangle, we can use the lengths of the sides of the triangle. In this case, we have a right triangle with two given side lengths: a 7 cm leg and a 15 cm leg.

Let's label the sides of the triangle: - The side opposite the angle we want to find the trigonometric ratios for is the opposite side. - The side adjacent to the angle is the adjacent side. - The hypotenuse is the side opposite the right angle.

In this case, the 7 cm leg is the adjacent side, and the 15 cm leg is the opposite side.

Calculating the Trigonometric Ratios

1. Sine (sin) of the angle: The sine of an angle is defined as the ratio of the length of the opposite side to the length of the hypotenuse. Therefore, we can calculate the sine of the angle using the given sides: sin(angle) = opposite/hypotenuse = 15/√(7^2 + 15^2).

2. Cosine (cos) of the angle: The cosine of an angle is defined as the ratio of the length of the adjacent side to the length of the hypotenuse. Therefore, we can calculate the cosine of the angle using the given sides: cos(angle) = adjacent/hypotenuse = 7/√(7^2 + 15^2).

3. Tangent (tan) of the angle: The tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side. Therefore, we can calculate the tangent of the angle using the given sides: tan(angle) = opposite/adjacent = 15/7.

Calculation Results

Using the given side lengths of 7 cm and 15 cm, we can calculate the trigonometric ratios as follows:

- Sine (sin) of the angle: sin(angle) = 15/√(7^2 + 15^2) - Cosine (cos) of the angle: cos(angle) = 7/√(7^2 + 15^2) - Tangent (tan) of the angle: tan(angle) = 15/7

Please note that these calculations assume the triangle is a right triangle and that the given side lengths