Question

В равнобокой трапеции острый угол равен 60 градусам,а боковая сторона-16см.Найдите основания трапеции,если их сумма равна 38 см. (Помогите срочно)

Answer 1

Обозначим трапецию: ABCD, провёдем высоты из вершин B и C, BB1 = CC1 - высоты, значит получим 2 равных прямоугольных треугольника ABB1 = DCC1, найдём катет C1D из определения косинуса нашего острого угла:
cos60=CD/C1D
C1D=16/2
C1D=8 = AB1
теперь запишем сторону AD по-другому: AB1+B1C1+C1D
и подставим всё в нашу формулу:
AB1+B1C1+C1D+BC=38, здесь B1C1=BC, т.к B1BCC1 - прямоугольник
2BC=22
BC=11, значит AC = 38-11=27

Answer 2

#### Task: Finding the bases of a trapezoid To find the bases of a trapezoid, we need to use the given information: the acute angle is 60 degrees, one of the lateral sides is 16 cm, and the sum of the bases is 38 cm. Let's denote the bases of the trapezoid as **b1** and **b2**. To solve this problem, we can use the following steps: 1. Use the given information to set up an equation. 2. Solve the equation to find the values of **b1** and **b2**. #### Setting up the equation In a trapezoid, the bases are parallel to each other. Since the trapezoid is isosceles (the acute angle is 60 degrees), the bases are equal in length. Let's assume the length of each base is **x**. According to the given information, one of the lateral sides is 16 cm. In an isosceles trapezoid, the lateral sides are equal in length. Therefore, the other lateral side is also 16 cm. Using this information, we can set up the following equation: **x + x + 16 + 16 = 38** Simplifying the equation, we get: **2x + 32 = 38** #### Solving the equation To solve the equation, we can follow these steps: 1. Subtract 32 from both sides of the equation: **2x = 38 - 32** Simplifying further: **2x = 6** 2. Divide both sides of the equation by 2: **x = 6 / 2** Simplifying further: **x = 3** Therefore, the length of each base of the trapezoid is **3 cm**. #### Answer The bases of the trapezoid are both **3 cm** in length. I hope this helps! Let me know if you have any further questions.