Question

Розв'яжіть трикутник АВС , якщо кут С=90°,АВ=6 см , ВС=3√2 см . ПОМОЖІТЬ УМОЛЯЮ!

Answer 1

Ответ:

розв'язати трикутник означає знайти всі його сторони і кути

за теоремою піфагора знайдемо АС

АС²=АВ²-ВС²=6²-(3√2)²=36-18=18

АС=√18=3√2

оскільки дві сторони цього трикутника однакові то він рівнобедренний і прямокутний тому 2 невідомі кути по 45°

Answer 2

Solving Triangle ABC

To solve triangle ABC, we are given the following information: - Angle C is 90°. - Side AB has a length of 6 cm. - Side BC has a length of 3√2 cm.

We can use the Pythagorean theorem and trigonometric ratios to find the missing side lengths and angles of the triangle.

Finding Side AC

To find side AC, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Let's denote side AC as 'c'. Using the Pythagorean theorem, we have:

c^2 = a^2 + b^2

In this case, side AB is 'a' and side BC is 'b'. Substituting the given values, we have:

c^2 = (6 cm)^2 + (3√2 cm)^2

Simplifying the equation, we get:

c^2 = 36 cm^2 + 18 cm^2

c^2 = 54 cm^2

Taking the square root of both sides, we find:

c ≈ √54 cm

c ≈ 7.35 cm

Therefore, side AC is approximately 7.35 cm.

Finding Angle A

To find angle A, we can use the trigonometric ratio of sine. In a right triangle, the sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse.

Let's denote angle A as 'α'. Using the sine ratio, we have:

sin(α) = opposite/hypotenuse

In this case, the side opposite angle A is side BC, and the hypotenuse is side AC. Substituting the given values, we have:

sin(α) = (3√2 cm) / (7.35 cm)

Using a calculator, we can find the value of sin(α) ≈ 0.617.

To find angle A, we can take the inverse sine (also known as arcsine) of this value:

α ≈ arcsin(0.617)

Using a calculator, we find that α ≈ 38.7°.

Therefore, angle A is approximately 38.7°.

Finding Angle B

To find angle B, we can use the fact that the sum of the angles in a triangle is always 180°.

Angle B = 180° - Angle A - Angle C

Substituting the given values, we have:

Angle B = 180° - 38.7° - 90°

Angle B ≈ 51.3°

Therefore, angle B is approximately 51.3°.

Summary

To summarize, we have solved triangle ABC with the given information: - Side AC is approximately 7.35 cm. - Angle A is approximately 38.7°. - Angle B is approximately 51.3°.

Please note that the values provided are approximate due to rounding.

I hope this helps! Let me know if you have any further questions.