Question

Помогите !! Срочно!! Даю много баллов ! Катет і гіпотенуза прямокутного трикутника відповідно дорівнюють 5см і 13см. Знайдіть а) синус кута, прилеглого до більшого катета; б) косинус кута, протилежного меншому катету; в) тангенс кута, протилежного більшому катету.

Answer 1

Ответ:

решение смотри на фотографии

Answer 2

To find the values of the trigonometric functions in a right triangle, we can use the lengths of the sides. In this case, the lengths of the legs (or catheti) are given as 5 cm and 13 cm. Let's calculate the requested values:

a) Sine of the angle adjacent to the larger leg (sin θ): The sine of an angle in a right triangle is defined as the ratio of the length of the opposite side to the length of the hypotenuse. In this case, the larger leg is the opposite side and the hypotenuse is the longest side of the triangle. Therefore, we can calculate the sine of the angle adjacent to the larger leg as:

sin θ = (opposite side) / (hypotenuse) = (5 cm) / (13 cm)

b) Cosine of the angle opposite the smaller leg (cos θ): The cosine of an angle in a right triangle is defined as the ratio of the length of the adjacent side to the length of the hypotenuse. In this case, the smaller leg is the adjacent side and the hypotenuse is the longest side of the triangle. Therefore, we can calculate the cosine of the angle opposite the smaller leg as:

cos θ = (adjacent side) / (hypotenuse) = (5 cm) / (13 cm)

c) Tangent of the angle opposite the larger leg (tan θ): The tangent of an angle in a right triangle is defined as the ratio of the length of the opposite side to the length of the adjacent side. In this case, the larger leg is the opposite side and the smaller leg is the adjacent side. Therefore, we can calculate the tangent of the angle opposite the larger leg as:

tan θ = (opposite side) / (adjacent side) = (5 cm) / (13 cm)

Let's calculate the values using the given lengths of the legs:

a) Sine of the angle adjacent to the larger leg (sin θ): sin θ = (5 cm) / (13 cm) = 0.3846 [[1]]

b) Cosine of the angle opposite the smaller leg (cos θ): cos θ = (5 cm) / (13 cm) = 0.3846 [[1]]

c) Tangent of the angle opposite the larger leg (tan θ): tan θ = (5 cm) / (13 cm) = 0.3846 [[1]]

Therefore, the values are: a) sin θ = 0.3846 b) cos θ = 0.3846 c) tan θ = 0.3846

Please let me know if there's anything else I can help you with!