Question

Розв’язати прямокутний трикутник з кутом 30° та гіпотенузою 5√3 см.

Answer 1

Ответ:

Объяснение:

катет, лежащий против угла в 30°, равен половине гипотенузы

значит один из катетов равен 5√(3)/2=2,5√(3) (см)

другой катет по теореме Пифагора равен √(5√(3)-2,5√(3))=

=√(2,5√(3)) (см)

Answer 2

Solving a Right Triangle with a 30° Angle and a Hypotenuse of 5√3 cm

To solve a right triangle with a 30° angle and a hypotenuse of 5√3 cm, we can use trigonometric functions to find the lengths of the other two sides of the triangle.

Step 1: Finding the Length of the Opposite Side (the side opposite the 30° angle)

We can use the sine function to find the length of the opposite side (often denoted as the "opposite" or "perpendicular" side). The sine of an angle in a right triangle is the ratio of the length of the opposite side to the length of the hypotenuse.

The formula for the sine function is: $$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$$

Substituting the given values: $$\sin(30°) = \frac{\text{opposite}}{5\sqrt{3}}$$

Solving for the length of the opposite side: $$\text{opposite} = 5\sqrt{3} \times \sin(30°)$$

Using the value of $\sin(30°)$ from trigonometric tables or a calculator, we can calculate the length of the opposite side.

Step 2: Finding the Length of the Adjacent Side (the side adjacent to the 30° angle)

We can use the cosine function to find the length of the adjacent side. The cosine of an angle in a right triangle is the ratio of the length of the adjacent side to the length of the hypotenuse.

The formula for the cosine function is: $$\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$$

Substituting the given values: $$\cos(30°) = \frac{\text{adjacent}}{5\sqrt{3}}$$

Solving for the length of the adjacent side: $$\text{adjacent} = 5\sqrt{3} \times \cos(30°)$$

Using the value of $\cos(30°)$ from trigonometric tables or a calculator, we can calculate the length of the adjacent side.

By following these steps, we can find the lengths of the opposite and adjacent sides of the right triangle.