Question

Пожалуйста помогите кто сможет буду очень благодарен даю 50 баллов. В треугольнике АВС угол А равен 40 градусов,угол С равен 75 градусов, ВС равен 17.Наидите неизветсные элементы треуголь

Answer 1

Могу найти только угол В. 
180 - 40 - 75 = 45 градусов.
Как найти стороны не знаю.

Answer 2

Given Information:

In triangle ABC, angle A is 40 degrees, angle C is 75 degrees, and side BC is 17 units.

Solution:

To find the unknown elements of the triangle, we can use the properties of triangles and trigonometry.

Finding Angle B:

The sum of the angles in a triangle is always 180 degrees. Therefore, we can find angle B by subtracting the sum of angles A and C from 180 degrees. Angle B = 180 degrees - (angle A + angle C) Angle B = 180 degrees - (40 degrees + 75 degrees) Angle B = 180 degrees - 115 degrees Angle B = 65 degrees

Finding Side AB:

To find side AB, we can use the Law of Sines, which states that the ratio of the length of a side to the sine of its opposite angle is constant for all sides and angles in a triangle. The Law of Sines can be written as: AB / sin(A) = BC / sin(B) Substituting the known values: AB / sin(40 degrees) = 17 / sin(65 degrees) Cross-multiplying: AB * sin(65 degrees) = 17 * sin(40 degrees) Dividing both sides by sin(65 degrees): AB = (17 * sin(40 degrees)) / sin(65 degrees) Using a calculator, we can find that AB ≈ 13.99 units.

Finding Side AC:

To find side AC, we can use the Law of Sines again: AC / sin(C) = BC / sin(B) Substituting the known values: AC / sin(75 degrees) = 17 / sin(65 degrees) Cross-multiplying: AC * sin(65 degrees) = 17 * sin(75 degrees) Dividing both sides by sin(65 degrees): AC = (17 * sin(75 degrees)) / sin(65 degrees) Using a calculator, we can find that AC ≈ 18.47 units.

Summary:

Based on the given information, we have determined the following: - Angle B is approximately 65 degrees. - Side AB is approximately 13.99 units. - Side AC is approximately 18.47 units.

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

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