Question

В прямоугольной трапеции острый угол равен 60° большая боковая сторона и большое основание равны по 20 см. Найти меньшее основание . Помогите

Answer 1

Трапеция АВСД, уголА=уголВ=90, уголД=60, АД=СД=20
пороводим высоту СК на АД, треугольник КСД прямоугольный, уголКСД=90-уголД=90-60=30, СД - гипотенуза , КД-катет лежит напротив угла 30 =1/2СД=20/2=10, АК=АД-КД=20-10=10, АВСК прямоугольник АК=ВС=10

Answer 2

Problem Analysis

We are given a right trapezoid with an acute angle of 60°. The larger side and the larger base of the trapezoid are both equal to 20 cm. We need to find the length of the smaller base.

Solution

To solve this problem, we can use trigonometric ratios in a right triangle formed by the height of the trapezoid and the smaller base.

Let's assume the smaller base of the trapezoid is denoted by 'x' cm. We can form a right triangle with the height of the trapezoid as the vertical side, the smaller base as the horizontal side, and the slant height as the hypotenuse.

Using trigonometric ratios, we can write the following equation: tan(60°) = height / x

Since we know that the larger side and the larger base are both equal to 20 cm, we can use the Pythagorean theorem to find the height of the trapezoid.

Let's solve the equation step by step:

1. Using the Pythagorean theorem, we can write: height^2 = (larger side)^2 - (smaller side)^2 height^2 = 20^2 - x^2 height^2 = 400 - x^2

2. Rearranging the equation, we have: x^2 + height^2 = 400

3. Substituting the value of height^2 from the trigonometric equation, we have: x^2 + tan^2(60°) * x^2 = 400

4. Simplifying the equation, we get: x^2(1 + tan^2(60°)) = 400

5. Using the trigonometric identity tan^2(60°) = 3, we have: x^2(1 + 3) = 400 4x^2 = 400

6. Solving for x, we find: x^2 = 100 x = √100 x = 10 cm

Answer

The length of the smaller base of the trapezoid is 10 cm.