Question

В равнобедренной трапеции большее основание 7 споловиной сантиметров Боковая сторона на 2 сантиметра а острый угол 60 градусов Найдите периметр этой трапеции

Answer 1

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Answer 2

Perimeter of an Isosceles Trapezoid

To find the perimeter of an isosceles trapezoid, we need to know the lengths of its bases and the lengths of its legs. In this case, we are given that the longer base of the trapezoid is 7.5 centimeters, the side is 2 centimeters, and the acute angle is 60 degrees.

To calculate the perimeter, we need to add up the lengths of all the sides of the trapezoid.

Calculating the Perimeter

The perimeter of an isosceles trapezoid can be calculated using the formula:

Perimeter = sum of the lengths of all sides

In this case, the trapezoid has two equal legs and two bases. Let's calculate the perimeter step by step:

1. Calculate the length of the shorter base: - Since the trapezoid is isosceles, the shorter base is also 7.5 centimeters.

2. Calculate the lengths of the legs: - The angle between the shorter base and one of the legs is 60 degrees. - We can use trigonometry to calculate the length of the leg. - The formula to calculate the length of a side in a right triangle is: side = hypotenuse * sin(angle). - In this case, the hypotenuse is the side of the trapezoid, which is 2 centimeters, and the angle is 60 degrees. - Using the formula, we can calculate the length of the leg.

3. Calculate the perimeter: - The perimeter is the sum of the lengths of all sides of the trapezoid. - Add the lengths of the two bases and the two legs to find the perimeter.

Let's calculate the perimeter using the given measurements.

Calculation

1. Length of the shorter base: 7.5 centimeters.

2. Length of the legs: - Using trigonometry, we can calculate the length of the leg using the formula side = hypotenuse * sin(angle). - In this case, the hypotenuse is 2 centimeters and the angle is 60 degrees. - Plugging in the values, we get: leg = 2 * sin(60). - Calculating the value, we find that the length of each leg is approximately 1.732 centimeters.

3. Perimeter: - The perimeter is the sum of the lengths of all sides of the trapezoid. - Add the lengths of the two bases and the two legs to find the perimeter. - The perimeter is calculated as follows: perimeter = 7.5 + 7.5 + 2 + 2 * 1.732. - Simplifying the expression, we find that the perimeter is approximately 21.464 centimeters.

Therefore, the perimeter of the given isosceles trapezoid is approximately 21.464 centimeters.

Please note that the calculations provided are based on the given information and may vary slightly depending on the exact measurements and rounding used.