Question

Дано: треугольник АВС ВС = 4см угол В =25°, угол А=40°. Найти уголС, АВ, АС-?

Answer 1

Сумма углов треугольника равна180 градусов. Значит, угол С= 180-(25+40)=180-65=115

Answer 2

Given Information:

We are given the following information about triangle ABC: - Side BC has a length of 4 cm. - Angle B is 25°. - Angle A is 40°.

We need to find the measures of angle C, side AB, and side AC.

Solution:

To find the measure of angle C, we can use the fact that the sum of the angles in a triangle is always 180°. Therefore, we can subtract the measures of angles A and B from 180° to find angle C: C = 180° - A - B.

To find the lengths of sides AB and AC, we can use trigonometric ratios. In particular, we can use the sine and tangent ratios.

1. Finding side AB: We can use the sine ratio to find the length of side AB. The sine ratio states that the sine of an angle is equal to the length of the side opposite the angle divided by the length of the hypotenuse. In this case, side AB is the side opposite angle A, and side AC is the hypotenuse. Therefore, we have: sin(A) = AB/AC.

2. Finding side AC: We can use the tangent ratio to find the length of side AC. The tangent ratio states that the tangent of an angle is equal to the length of the side opposite the angle divided by the length of the side adjacent to the angle. In this case, side BC is the side opposite angle A, and side AB is the side adjacent to angle A. Therefore, we have: tan(A) = BC/AB.

Let's calculate the values of angle C, side AB, and side AC using the given information and the trigonometric ratios.

Calculation:

1. Angle C: Using the formula C = 180° - A - B, we can substitute the given values: C = 180° - 40° - 25° = 115°.

2. Side AB: Using the formula sin(A) = AB/AC, we can substitute the given values: sin(40°) = AB/AC. To find AB, we need to rearrange the equation: AB = AC * sin(40°).

3. Side AC: Using the formula tan(A) = BC/AB, we can substitute the given values: tan(40°) = BC/AB. To find AC, we need to rearrange the equation: AC = BC / tan(40°).

Let's calculate the values of AB and AC using the given values.

Calculation:

1. Side AB: AB = AC * sin(40°). AB = 4 cm * sin(40°). AB ≈ 2.57 cm.

2. Side AC: AC = BC / tan(40°). AC = 4 cm / tan(40°). AC ≈ 4.95 cm.

Therefore, the values we have calculated are: - Angle C ≈ 115°. - Side AB ≈ 2.57 cm. - Side AC ≈ 4.95 cm.

Please note that the calculations are approximations and rounded to two decimal places.

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