Question

Дано: АВСD - трапеция, АD = 10см, ВС = 6см, угол D = 45 градусов, угол А = 90 градусов. Найти: СD

Answer 1

Решение смотри в файле.

Answer 2

Я надеюсь ,что правильно .

Answer 3

Given Information:

We are given that ABCD is a trapezoid, AD = 10 cm, BC = 6 cm, angle D = 45 degrees, and angle A = 90 degrees. We need to find CD.

Solution:

To find CD, we can use the properties of a trapezoid and the given information.

From the properties of a trapezoid, we know that the opposite sides are parallel. Therefore, CD || AB.

Since angle A = 90 degrees, angle D = 45 degrees, and angle ACD is an exterior angle of triangle ABD, we can use the angle sum property of triangles to find angle ACD.

Angle ACD = angle A + angle D = 90 degrees + 45 degrees = 135 degrees.

Now, we can use the sine rule in triangle ACD to find CD.

The sine rule states that in a triangle ABC, the ratio of the length of a side to the sine of its opposite angle is constant.

In triangle ACD, we have: AC/CD = sin(angle ACD)

Substituting the known values: AC/CD = sin(135 degrees)

Using the value of sin(135 degrees) from a trigonometric table or calculator, we find that sin(135 degrees) = 0.7071.

Therefore, we have: AC/CD = 0.7071

Since AC = AD + CD and AD = 10 cm, we can substitute the values: (10 + CD)/CD = 0.7071

Simplifying the equation: 10 + CD = 0.7071 * CD 10 = 0.7071 * CD - CD 10 = (0.7071 - 1) * CD 10 = -0.2929 * CD CD = 10 / -0.2929

Calculating the value of CD: CD ≈ -34.15 cm

Answer:

The length of CD is approximately -34.15 cm.