Question

Основи трапеції дорівнюють 8 см і 15 см одна з бічних сторін трапеції дорівнює 8 см і утворює з меншою основою кут 120° знайдіть діагоналі трапеції

Answer 1

Ответ:

см фото

Объяснение:

Answer 2

Calculation of the Diagonals of a Trapezoid

To find the diagonals of a trapezoid, we can use the given information about the side lengths and angle of the trapezoid. Let's solve the problem step by step.

Given information: - One of the side lengths of the trapezoid is 8 cm. - The other side length of the trapezoid is 15 cm. - The angle formed by the smaller base and one of the side lengths is 120°.

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

1. Diagonal 1 (d1): - Formula: d1 = √(a^2 + b^2 - 2abcosθ) - Where: - a = length of one of the bases - b = length of one of the side lengths - θ = angle between the bases

2. Diagonal 2 (d2): - Formula: d2 = √(c^2 + b^2 + 2cbcosθ) - Where: - c = difference between the lengths of the bases (c = |a - b|) - b = length of one of the side lengths - θ = angle between the bases

Let's substitute the given values into the formulas to find the diagonals.

Using the given information: - Length of one of the bases (a) = 8 cm - Length of one of the side lengths (b) = 15 cm - Angle between the bases (θ) = 120°

Calculating the diagonals:

1. Diagonal 1 (d1): - Substituting the values into the formula: - d1 = √(8^2 + 15^2 - 2 * 8 * 15 * cos(120°)) - Evaluating the expression: - d1 = √(64 + 225 - 240 * (-0.5)) - d1 = √(64 + 225 + 120) - d1 = √(409) - d1 ≈ 20.22 cm

2. Diagonal 2 (d2): - Calculating the difference between the lengths of the bases: - c = |8 - 15| = 7 cm - Substituting the values into the formula: - d2 = √(7^2 + 15^2 + 2 * 7 * 15 * cos(120°)) - Evaluating the expression: - d2 = √(49 + 225 + 210 * (-0.5)) - d2 = √(49 + 225 - 105) - d2 = √(169) - d2 = 13 cm

Therefore, the diagonals of the trapezoid are approximately 20.22 cm and 13 cm.

Please note that the calculations are based on the given information and the formulas for finding the diagonals of a trapezoid.