Question

Основания равнобедренной трапеции равны 13см и 28 см . Острый угол равен 60° . Найдите периметер трапеции

Answer 1

28-13=15-это разница между основаниями, потом подели 15 на 2,15/2=7,5!То что ты получил есть малый катет, лежащий против угла в 30 градусов, так как треугольник прямоугольный 90-60=30!Следовательно гипотенуза равна 7.5*2=15!Таких боковых сторон две, поэтому 15*2=30!Р=30+13+28=71!

Answer 2

Given Information:

We are given that the bases of the isosceles trapezoid are 13 cm and 28 cm, and that one of the acute angles is 60°.

Solution:

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

Let's label the trapezoid as ABCD, where AB and CD are the bases, and AD and BC are the legs.

Since the trapezoid is isosceles, we know that AB = CD. Therefore, AB = 13 cm and CD = 28 cm.

To find the lengths of the legs AD and BC, we can use the properties of an isosceles trapezoid. In an isosceles trapezoid, the diagonals are congruent, and the angles between the bases and the diagonals are equal.

Since one of the acute angles is given as 60°, we can conclude that the other acute angle is also 60°. Therefore, triangle ABD is an equilateral triangle, and triangle BCD is an isosceles triangle.

Let's find the length of AD using trigonometry. In triangle ABD, we have an angle of 60° and a side length of 13 cm. The side opposite the given angle is AD. We can use the sine function to find AD:

sin(60°) = AD / 13

Simplifying the equation, we get:

AD = 13 * sin(60°)

To find the length of BC, we can use the fact that triangle BCD is an isosceles triangle. The base angles of an isosceles triangle are congruent. Therefore, angle BCD is also 60°. We can use the sine function again to find BC:

sin(60°) = BC / 28

Simplifying the equation, we get:

BC = 28 * sin(60°)

Now that we have the lengths of all four sides, we can find the perimeter of the trapezoid by adding them up:

Perimeter = AB + BC + CD + AD

Substituting the values we found earlier:

Perimeter = 13 + (28 * sin(60°)) + 28 + (13 * sin(60°))

Calculating the values:

Perimeter = 13 + (28 * 0.866) + 28 + (13 * 0.866)

Perimeter = 13 + 24.248 + 28 + 11.258

Perimeter = 76.506 cm

Therefore, the perimeter of the trapezoid is 76.506 cm.

Answer:

The perimeter of the trapezoid is 76.506 cm.