Question

знайти площу прямокутника, якщо його діагональ дорівнює 10√3 см і утворює кут 30° з більшою стороною..​

Answer 1

Ответ:

Двно: АБСД - прямокутник, АС=10√3, кут С =30°. Знайти: SквадраАБСД. Розвязанняи: СД=Аб= АС/2=5√3. За т. Піфагора.

АБ=БС=√(АС)²-(СД)²*15

S=Ад*аб*15*5√3=75√3.

Answer 2

Finding the Area of a Rectangle with a Given Diagonal and Angle

To find the area of a rectangle when its diagonal is given as 10√3 cm and it forms a 30° angle with the longer side, we can use trigonometry and the properties of a rectangle.

Let's break down the problem step by step:

1. Identify the given information: - Diagonal of the rectangle = 10√3 cm - Angle formed by the diagonal and the longer side = 30°

2. Understand the properties of a rectangle: - A rectangle is a quadrilateral with four right angles. - The opposite sides of a rectangle are equal in length. - The diagonals of a rectangle are equal in length and bisect each other.

3. Use trigonometry to find the lengths of the sides: - Let's assume the longer side of the rectangle is 'a' and the shorter side is 'b'. - We can use the given angle of 30° to find the lengths of the sides using trigonometric ratios. - The longer side 'a' is adjacent to the angle, so we can use the cosine function: cos(30°) = a / (10√3). - Solving for 'a', we get: a = (10√3) * cos(30°).

4. Calculate the area of the rectangle: - The area of a rectangle is given by the formula: Area = length * width. - In this case, the longer side 'a' is the length and the shorter side 'b' is the width. - Since the opposite sides of a rectangle are equal, we have: a = b. - Therefore, the area of the rectangle is: Area = a * a = a^2.

5. Substitute the value of 'a' into the area formula: - Using the value of 'a' we found earlier, we can calculate the area of the rectangle.

Let's calculate the area of the rectangle using the above steps.

Calculation:

1. Using trigonometry, we found that: a = (10√3) * cos(30°).

2. Substituting the value of cos(30°) = √3 / 2, we get: a = (10√3) * (√3 / 2) = 15 cm.

3. The area of the rectangle is: Area = a^2 = 15^2 = 225 cm^2.

Therefore, the area of the rectangle is 225 square centimeters.

Please let me know if you need any further assistance!