Question

В ромбе сто­ро­на равна 10, одна из диа­го­на­лей — 10 корень из 3 , а угол, из ко­то­ро­го вы­хо­дит эта диа­го­наль, равен 60°. Най­ди­те пло­щадь ромба, де­лен­ную на корень из 3

Answer 1

Вавпапа па вра рв апа ва 

Answer 2

Calculation of the Area of a Rhombus

To find the area of a rhombus, we can use the formula: Area = (diagonal1 * diagonal2) / 2.

Given the information provided: - One side of the rhombus is equal to 10. - One of the diagonals is equal to 10 * √3. - The angle from which this diagonal originates is 60°.

Let's calculate the area of the rhombus step by step.

1. Find the length of the other diagonal: - Since the angle from which the diagonal originates is 60°, we can use the Law of Cosines to find the length of the other diagonal. - The Law of Cosines states that for a triangle with sides a, b, and c, and angle C opposite side c, the following equation holds: c^2 = a^2 + b^2 - 2ab * cos(C). - In our case, a = 10, b = 10 * √3, and C = 60°. - Plugging in the values, we have: c^2 = 10^2 + (10 * √3)^2 - 2 * 10 * (10 * √3) * cos(60°). - Simplifying the equation, we get: c^2 = 100 + 300 - 200 * √3 * 0.5. - Further simplification gives: c^2 = 400 - 100√3. - Taking the square root of both sides, we find: c ≈ √(400 - 100√3).

2. Calculate the area of the rhombus: - Using the formula for the area of a rhombus, we have: Area = (diagonal1 * diagonal2) / 2. - Plugging in the values, we get: Area = (10 * √3 * √(400 - 100√3)) / 2. - Simplifying the equation, we have: Area = 5 * √3 * √(400 - 100√3).

Therefore, the area of the rhombus, divided by √3, is approximately 5 * √(400 - 100√3).

Please note that the calculations provided are based on the information given and may not be exact due to rounding.

Let me know if there's anything else I can help you with!