Question

У рівнобічної трапеції з гострим кутом 60° сума основ дорівнює 86 см, а бічна сторона 22 см. Знайдіть основи трапеції

Answer 1

Чертеж и решение на фото:

Answer 2

Finding the bases of an isosceles trapezoid

To find the bases of an isosceles trapezoid, we can use the given information about the acute angle and the sum of the bases.

Let's denote the length of the longer base as b and the length of the shorter base as a. We are given that the acute angle of the trapezoid is 60°, the sum of the bases is 86 cm, and the length of the lateral side is 22 cm.

To find the bases, we can use the following formulas:

1. b + a = 86 cm (sum of the bases) 2. a = b - 2h (where h is the height of the trapezoid)

To find the height of the trapezoid, we can use the Pythagorean theorem:

3. h = √(lateral side^2 - (0.5 * (b - a))^2)

Let's calculate the values step by step.

Calculating the height of the trapezoid

Using the Pythagorean theorem, we can calculate the height of the trapezoid:

h = √(22 cm^2 - (0.5 * (b - a))^2)

Calculating the bases of the trapezoid

Now, let's substitute the value of h into equation 2 to find a:

a = b - 2h

Substituting the value of a into equation 1, we can solve for b:

b + (b - 2h) = 86 cm

Simplifying the equation, we get:

2b - 2h = 86 cm

Now, we can solve this equation for b.

Final calculations

Let's calculate the values using the given information.

Given: - Acute angle: 60° - Sum of the bases: 86 cm - Lateral side: 22 cm

Using the formulas and calculations mentioned above, we can find the values of a and b.

Please wait while I perform the calculations.