Question

Дано: CosB=3/7;AC=21 Найти AB​

Answer 1

Ответ:

Треугольник АВС является прямоугольным (∠С = 90°), АВ = 21 см, sin B = 3/7, по решениям прямоугольных треугольников: катет равен произведению гипотенузы на синус противолежащего угла, значит АС = АВ * sin B = 21 см * 3/7 = 9 см

Объяснение:

Answer 2

To find the length of AB, we can use the cosine rule, which states:

c^2 = a^2 + b^2 - 2ab * cos(C)

In this case, we have the following information:

Cos(B) = 3/7 AC = 21

Let's assume that AB is represented by the variable x. Now, we can set up the equation:

x^2 = 21^2 + b^2 - 2 * 21 * b * cos(B)

Since Cos(B) = 3/7, we can substitute it into the equation:

x^2 = 21^2 + b^2 - 2 * 21 * b * (3/7)

Simplifying further:

x^2 = 441 + b^2 - (6/7) * 21 * b x^2 = 441 + b^2 - 18b

Now, let's solve for b by isolating it:

b^2 - 18b + 441 - x^2 = 0

This is a quadratic equation. We can use the quadratic formula to solve for b:

b = (-(-18) ± sqrt((-18)^2 - 4 * 1 * (441 - x^2))) / (2 * 1) b = (18 ± sqrt(324 - 4(441 - x^2))) / 2 b = (18 ± sqrt(324 - 1764 + 4x^2)) / 2 b = (18 ± sqrt(4x^2 - 1440)) / 2 b = (18 ± sqrt(4(x^2 - 360))) / 2 b = 9 ± sqrt(x^2 - 360)

Since AB represents a distance, b cannot be negative. Therefore, we can rewrite the equation as:

b = 9 + sqrt(x^2 - 360)

Now, substitute this expression for b in the original equation:

x^2 = 441 + (9 + sqrt(x^2 - 360))^2 - 18(9 + sqrt(x^2 - 360))

Expand and simplify:

x^2 = 441 + 81 + 18sqrt(x^2 - 360) + (x^2 - 360) - 162 - 18sqrt(x^2 - 360) x^2 = x^2 + 81 + 81 - 360 - 162 x^2 = 2x^2 - 360

Rearrange the equation:

x^2 = 360

Take the square root of both sides:

x = ±sqrt(360)

x ≈ ±18.97

Since the length of a line segment cannot be negative, the length of AB is approximately 18.97.