Question

Найдите боковые стороны стороны равнобедренной трапеции ,основание которой равны 14 см и 8 см ,а один из углов равен 120 градусов .

Answer 1

Лови решение:) Была рада помочь!

Answer 2

Finding the Sides of an Isosceles Trapezoid

To find the side lengths of the given isosceles trapezoid with bases of 14 cm and 8 cm, and one angle measuring 120 degrees, we can use the properties of an isosceles trapezoid to calculate the side lengths.

The properties of an isosceles trapezoid are: 1. The non-parallel sides are congruent. 2. The base angles are congruent.

Calculating the Side Lengths

Given: - Base 1 (larger base) = 14 cm - Base 2 (smaller base) = 8 cm - One angle = 120 degrees

We can use the following steps to calculate the side lengths: 1. Calculate the length of the non-parallel sides using the given bases and the angle. 2. Use the properties of an isosceles trapezoid to verify the calculated side lengths.

Step 1: Calculating the Length of the Non-Parallel Sides

Using the given information, we can calculate the length of the non-parallel sides using trigonometric functions.

Let's denote the length of the non-parallel sides as 'a' and 'b'.

Using the given angle of 120 degrees and the lengths of the bases, we can use trigonometric functions to calculate the side lengths.

Using the law of cosines: - a^2 = b^2 + c^2 - 2bc * cos(A) - where a and b are the side lengths, and A is the given angle.

Substituting the given values: - a^2 = 8^2 + 14^2 - 2*8*14 * cos(120)

Solving for 'a': - a = sqrt(8^2 + 14^2 - 2*8*14 * cos(120))

Step 2: Verifying the Calculated Side Lengths

We can now verify the calculated side lengths using the properties of an isosceles trapezoid.

The properties state that the non-parallel sides should be congruent. We can compare the calculated side lengths to confirm if they are equal.

Conclusion

By following the steps outlined above, we can calculate the side lengths of the given isosceles trapezoid with bases of 14 cm and 8 cm, and one angle measuring 120 degrees.