Question

Дан прямоугольный треугольник АВС, если угол С-прямой , АВ=13см, АС=12см. Найти косинус угла В, тангенс угла В. СРОЧНО!!!

Answer 1

Ответ:

soc ∠B=$\frac{5}{13}$

tg ∠B =2,4

Объяснение:

Answer 2

Given Information

We are given a right triangle ABC, where angle C is a right angle. We are also given that AB = 13 cm and AC = 12 cm.

Solution

To find the cosine and tangent of angle B, we can use the trigonometric ratios.

Cosine of Angle B

The cosine of an angle in a right triangle is defined as the ratio of the length of the adjacent side to the hypotenuse. In this case, the adjacent side to angle B is AB and the hypotenuse is AC.

Therefore, the cosine of angle B can be calculated as:

cos(B) = AB / AC

Substituting the given values, we have:

cos(B) = 13 cm / 12 cm

To simplify the calculation, we can convert the lengths to a common unit, such as meters:

cos(B) = 0.1083

Tangent of Angle B

The tangent of an angle in a right triangle is defined as the ratio of the length of the opposite side to the adjacent side. In this case, the opposite side to angle B is BC and the adjacent side is AB.

Therefore, the tangent of angle B can be calculated as:

tan(B) = BC / AB

To find the length of 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.

In this case, we have:

AC^2 = AB^2 + BC^2

Substituting the given values, we have:

(12 cm)^2 = (13 cm)^2 + BC^2

Simplifying the equation, we get:

BC^2 = (12 cm)^2 - (13 cm)^2

Solving for BC, we find:

BC ≈ 5.385 cm

Now, we can substitute the values of BC and AB into the equation for the tangent of angle B:

tan(B) = BC / AB

Substituting the values, we have:

tan(B) ≈ 5.385 cm / 13 cm

To simplify the calculation, we can convert the lengths to a common unit, such as meters:

tan(B) ≈ 0.4142

Summary

The cosine of angle B is approximately 0.1083 and the tangent of angle B is approximately 0.4142.

Please note that the calculations are approximate due to rounding.