Question

Стороны прямоугольника равны 6√2 и 6√6 найдите углы которые образуют диагональ со сторонами треугольника ​

Answer 1

Відповідь:

90°,30°,60°

Пояснення:

Знайдемо діагональ трикутникаАВС:  АС=√АВ²+ВС²⇒√288⇒√144*2=12√2

з трикутникаАВС  знайдемо ∠С    6√2/12/2=Sin∠C       ∠C=30°

тоді ∠А=180-90-30=60

Answer 2

Finding the Angles Formed by the Diagonal of a Rectangle

To find the angles formed by the diagonal of a rectangle with sides of length 6√2 and 6√6, we can use trigonometric principles.

First, let's find the length of the diagonal using the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

The length of the diagonal (d) can be found using the formula: d = √(a^2 + b^2), where a and b are the lengths of the sides of the rectangle.

Using the given side lengths: a = 6√2 and b = 6√6

We can calculate the length of the diagonal: d = √((6√2)^2 + (6√6)^2)

Calculating: d = √(72 + 216) = √288 = 12√2

So, the length of the diagonal is 12√2.

Now, to find the angles formed by the diagonal with the sides of the rectangle, we can use trigonometric functions. The tangent of an angle in a right-angled triangle is the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.

Let's denote the angles formed by the diagonal with the sides of the rectangle as θ1 and θ2.

The tangent of an angle can be expressed as: tan(θ) = opposite/adjacent

For the first angle (θ1): tan(θ1) = (6√2)/(6√6) = √(2/6) = √(1/3) = 1/√3

For the second angle (θ2): tan(θ2) = (6√6)/(6√2) = √(6/2) = √3

So, the angles formed by the diagonal with the sides of the rectangle are: θ1 = arctan(1/√3) and θ2 = arctan(√3)

Using a calculator, we can find the approximate values of these angles.

Let's calculate the approximate values of θ1 and θ2.