Question

В ПРЯМОУГОЛЬНОМ ТРЕУГОЛЬНИКЕ АВС УГОЛ С = 90 ГРАДУСОВ, УГОЛ А = 60 ГРАДУСОВ, АС = 12 СМ. НАЙДИТЕ АВ, ВС И УГОЛ В

Answer 1

180-60-90=30(уголВ). Катет,против 30 градусов равен половине гипотенузы.=>12*2=24(ВА). По теор Пифаг:12^2+х^2=24^2 144+х^2=576 Х^2=432 Х=12(корень 3)-ВС

Answer 2

Given Information:

We are given a right triangle ABC, where angle C is 90 degrees, angle A is 60 degrees, and side AC is 12 cm. We need to find the lengths of sides AB and BC, as well as angle B.

Solution:

To solve this problem, we can use the properties of right triangles and trigonometric ratios.

Finding Side AB:

We can use the trigonometric ratio sine (sin) to find the length of side AB. The sine of angle A is equal to the ratio of the length of the side opposite angle A (AB) to the length of the hypotenuse (AC).

Using the given information: - Angle A = 60 degrees - Side AC = 12 cm

We can set up the equation: sin(A) = AB / AC

Substituting the values: sin(60) = AB / 12

Using a calculator, we can find the value of sin(60) to be approximately 0.866.

Solving for AB: 0.866 = AB / 12

Cross-multiplying: AB = 0.866 * 12

Calculating: AB ≈ 10.392 cm

Therefore, the length of side AB is approximately 10.392 cm.

Finding Side BC:

To find the length of side BC, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

Using the given information: - Side AC = 12 cm

We can set up the equation: AC^2 = AB^2 + BC^2

Substituting the values: 12^2 = 10.392^2 + BC^2

Simplifying: 144 = 107.768 + BC^2

Rearranging the equation: BC^2 = 144 - 107.768

Calculating: BC^2 ≈ 36.232

Taking the square root of both sides: BC ≈ √36.232

Calculating: BC ≈ 6.02 cm

Therefore, the length of side BC is approximately 6.02 cm.

Finding Angle B:

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

Using the given information: - Angle C = 90 degrees - Angle A = 60 degrees

We can set up the equation: Angle B = 180 - Angle C - Angle A

Substituting the values: Angle B = 180 - 90 - 60

Calculating: Angle B = 30 degrees

Therefore, angle B is 30 degrees.

Summary:

In the given right triangle ABC, where angle C is 90 degrees, angle A is 60 degrees, and side AC is 12 cm, we have found the following: - Length of side AB ≈ 10.392 cm - Length of side BC ≈ 6.02 cm - Angle B = 30 degrees