Question

Дана трапеция ABCD, в которой угол C = углу D= 90°, AB = 9 см, BD=12 см и AD=15см. Найдите синус и косинус угла CBD. Помогите пожалуйста очень нужно, ДАЮ 50 БАЛЛОВ.если можно с чертежом​

Answer 1

Ответ:

sinx= 0,6 ; cosx= 0,8

Объяснение:

Как решил?

Шаг 1. Находим высоту трапеции , которая кстати равна стороне CD. Находится она хитрым способом уравнения ( на фото видно)

Шаг 2. Зная , высоту и стороны треугольника расписываем синус и косинус угла.

Answer 2

Solving for the Sine and Cosine of Angle CBD in Trapezoid ABCD

To solve for the sine and cosine of angle CBD in trapezoid ABCD, we can use the given measurements and trigonometric principles.

Given: - Trapezoid ABCD - Angle C = Angle D = 90° - AB = 9 cm - BD = 12 cm - AD = 15 cm

Finding the Sine of Angle CBD

The sine of an angle in a right-angled triangle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse.

In triangle CBD: - The side opposite angle CBD is BD - The hypotenuse is CD

Using the Pythagorean theorem, we can find the length of CD: ``` CD^2 = BD^2 + BC^2 CD^2 = 12^2 + (AD - AB)^2 CD^2 = 144 + (15 - 9)^2 CD^2 = 144 + 36 CD^2 = 180 CD = sqrt(180) CD = 6 * sqrt(5) ``` Now, we can find the sine of angle CBD: ``` sin(CBD) = BD / CD sin(CBD) = 12 / (6 * sqrt(5)) sin(CBD) = 2 / sqrt(5) ``` So, the sine of angle CBD is 2 / sqrt(5).

Finding the Cosine of Angle CBD

The cosine of an angle in a right-angled triangle is defined as the ratio of the length of the side adjacent to the angle to the length of the hypotenuse.

In triangle CBD: - The side adjacent to angle CBD is BC - The hypotenuse is CD

We already found the length of CD in the previous calculation.

Now, we can find the cosine of angle CBD: ``` cos(CBD) = BC / CD cos(CBD) = (AD - AB) / CD cos(CBD) = (15 - 9) / (6 * sqrt(5)) cos(CBD) = 6 / (6 * sqrt(5)) cos(CBD) = 1 / sqrt(5) ``` So, the cosine of angle CBD is 1 / sqrt(5).

Conclusion

In trapezoid ABCD, with the given measurements, the sine of angle CBD is 2 / sqrt(5) and the cosine of angle CBD is 1 / sqrt(5).