Question

В треугольнике АВС АС=ВС=4 корень из 5,АВ=16. Найти tgA

Answer 1

Треугольник АВС-равнобедренный т.к.АС=ВС угол при основании равнобедренного тр-ка =45гр   а tg45=1

Answer 2

Given Information

We are given that in triangle ABC, AC = BC = 4√5 and AB = 16.

Finding tgA

To find tgA, we need to determine the value of angle A.

To do this, we can use the Law of Cosines, which states that in a triangle with sides a, b, and c, and angle C opposite side c, the following equation holds:

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

In our case, we have: AC^2 = AB^2 + BC^2 - 2 * AB * BC * cos(A)

Substituting the given values, we get: (4√5)^2 = 16^2 + 4√5^2 - 2 * 16 * 4√5 * cos(A)

Simplifying the equation: 80 = 256 + 20 - 128√5 * cos(A) 80 = 276 - 128√5 * cos(A)

Rearranging the equation: 128√5 * cos(A) = 276 - 80 128√5 * cos(A) = 196

Dividing both sides by 128√5: cos(A) = 196 / (128√5)

Now, we can use the trigonometric identity: tg(A) = sin(A) / cos(A)

Since we have the value of cos(A), we can find sin(A) using the Pythagorean identity: sin^2(A) + cos^2(A) = 1

Substituting the value of cos(A) and solving for sin(A): sin^2(A) + (196 / (128√5))^2 = 1 sin^2(A) + 38416 / (128^2 * 5) = 1 sin^2(A) + 38416 / 163840 = 1 sin^2(A) + 0.23498535156 = 1 sin^2(A) = 1 - 0.23498535156 sin^2(A) = 0.76501464844 sin(A) = √(0.76501464844) sin(A) ≈ 0.874007

Now, we can find tg(A): tg(A) = sin(A) / cos(A) tg(A) = 0.874007 / (196 / (128√5)) tg(A) = 0.874007 * (128√5 / 196) tg(A) ≈ 0.874007 * 0.924678 tg(A) ≈ 0.807086

Therefore, tgA ≈ 0.807086.

Note: The calculations provided above are based on the given information and mathematical formulas.