Question

найдите меньшее основание равнобедренной трапеции, если ее большее оснрвание равно 16см боковая сторона 10см а один из углов равен 60 градусов.

Answer 1

Пускай АВСД Трапеция. Опустим высоты ВК и СМ ВС=КМ. В треугольнике АВК угол АВК=30 градусов, (180-90-60), значит 2*АК=АВ, 2*АК=10, АК=5 см, АК=МД=5 см, ВС=КМ=АД-АК-МД=16-5-5=6 см.

Answer 2

Finding the Smaller Base of an Isosceles Trapezoid

To find the smaller base of an isosceles trapezoid, we can use the given information: the larger base is 16 cm, one of the lateral sides is 10 cm, and one of the angles is 60 degrees.

First, let's calculate the smaller base using the given information.

Step 1: Calculate the Height of the Trapezoid The height of the trapezoid can be calculated using the formula: \[ h = a \times \sin(\theta) \] where \( a \) is the length of one of the lateral sides and \( \theta \) is the angle between the lateral side and the larger base.

Using the given values: \[ h = 10 \times \sin(60^\circ) \] \[ h = 10 \times \frac{\sqrt{3}}{2} \] \[ h = 5\sqrt{3} \]

Step 2: Calculate the Area of the Trapezoid The area of the trapezoid can be calculated using the formula: \[ A = \frac{1}{2} \times (a + b) \times h \] where \( a \) and \( b \) are the lengths of the two parallel sides and \( h \) is the height.

Using the given values: \[ A = \frac{1}{2} \times (16 + b) \times 5\sqrt{3} \] \[ 108 = (16 + b) \times \sqrt{3} \] \[ 108\sqrt{3} = 16\sqrt{3} + b\sqrt{3} \] \[ 108\sqrt{3} - 16\sqrt{3} = b\sqrt{3} \] \[ 92\sqrt{3} = b\sqrt{3} \] \[ b = 92 \]

Step 3: Conclusion The length of the smaller base of the isosceles trapezoid is 92 cm.