Question

В треугольнике авс угол с равен 90 градусов, ас=5,6; тангенс а=24/7. найти ав

Answer 1

Тангенс =ВС/АС ; АС=тангенс*Вс=24/17*5,6=19,2
по теореме Пифагора: АВ=кореньВС в квадрате+АС в квадрате=корень 19,2 в квадрате+5,6 в квадрате=20
АВ=20

Answer 2

Task: Find the value of angle A in triangle ABC, given that angle C is 90 degrees, AC is 5.6, and the tangent of angle A is 24/7.

To find the value of angle A in triangle ABC, we can use the given information and trigonometric ratios.

Let's start by using the tangent ratio:

Tangent of angle A = opposite side / adjacent side

Given that the tangent of angle A is 24/7, we can set up the following equation:

24/7 = opposite side / adjacent side

Now, let's use the Pythagorean theorem to relate the sides of the triangle:

In a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

a^2 + b^2 = c^2

In our case, angle C is 90 degrees, so the side opposite angle C is the hypotenuse.

Now, let's substitute the given values into the equation:

AC^2 = AB^2 + BC^2

5.6^2 = AB^2 + BC^2

Simplifying the equation, we have:

31.36 = AB^2 + BC^2

Now, we can substitute the values into the equation for the tangent ratio:

24/7 = AB / BC

Rearranging the equation, we have:

AB = (24/7) * BC

Now, we can substitute this value of AB into the Pythagorean theorem equation:

31.36 = [(24/7) * BC]^2 + BC^2

Simplifying the equation, we have:

31.36 = (576/49) * BC^2 + BC^2

Combining like terms, we have:

31.36 = (625/49) * BC^2

Now, let's solve for BC:

BC^2 = (31.36 * 49) / 625

Taking the square root of both sides, we have:

BC = sqrt((31.36 * 49) / 625)

Now, we can substitute this value of BC into the equation for AB:

AB = (24/7) * BC

Finally, we can find the value of angle A using the tangent ratio:

tan(A) = opposite side / adjacent side

tan(A) = AB / BC

tan(A) = [(24/7) * BC] / BC

tan(A) = 24/7

To find the value of angle A, we can take the inverse tangent (arctan) of 24/7:

A = arctan(24/7)

Using a calculator, we find that:

A ≈ 73.74 degrees

Therefore, the value of angle A in triangle ABC is approximately 73.74 degrees.

Please note that the calculations provided are based on the given information and assumptions.