Question

В равнобердренной трапеции большее основание равно 56см боковая сторона равна 26 см угол между ними 60 градусов найдите меньшее основание

Answer 1

Ответ:

АВ=СД=26см, уголВАД=60градусов, ВН - высота

в прямоугольном треугольникеАВН: уголАВН=90-60=30градусов

мы знаем, что катет, лежащий против угла 30 градусов, равен половине гипотенузы, следовательно, АН=26:2=13см

АН=РД=13см (т.к. треугАВН=треугСРД)

ВС=НР=56-13-13=30см

Пошаговое объяснение:

УголАВН=90-60=30градусов

УголВАД=60градусов

АВ=СД=26см

АН=13(26:2)

РД=Треугольник СРД

ВС-НР=56-13-13=30см

Answer 2

Finding the Length of the Smaller Base in an Isosceles Trapezoid

To find the length of the smaller base in an isosceles trapezoid, we can use the given information about the larger base, the side length, and the angle between them.

Let's break down the given information: - Larger base = 56 cm - Side length = 26 cm - Angle between the larger base and the side = 60 degrees

To find the length of the smaller base, we can use the trigonometric relationship between the side length, the angle, and the lengths of the bases in a trapezoid.

The formula we can use is:

Smaller base = Larger base - 2 * (side length * sin(angle)) Now let's substitute the given values into the formula:

Smaller base = 56 cm - 2 * (26 cm * sin(60 degrees))

To calculate the value, we need to find the sine of 60 degrees. From the trigonometric table, we know that sin(60 degrees) = 0.866.

Substituting this value into the formula:

Smaller base = 56 cm - 2 * (26 cm * 0.866) Smaller base = 56 cm - 2 * 22.616 cm Smaller base = 56 cm - 45.232 cm Smaller base = 10.768 cm

Therefore, the length of the smaller base in the given isosceles trapezoid is 10.768 cm.

I hope this helps! Let me know if you have any further questions.