Question

Помогите блин уже часа два сижу не могу решить 1.В треугольнике АВС угол С =90°,tgA=2√6 найти cosA

Answer 1

Ab^2=4+21=25
ab=корень из 25 и равно 5 
косинус равен 2/5=0,4

Answer 2

Finding cosA in a right triangle

To find cosA in a right triangle ABC, where angle C is 90° and tgA = 2√6, we can use the trigonometric identity:

cos^2A + sin^2A = 1

Since angle C is 90°, we know that sinA = cosC and cosA = sinC. Therefore, we can rewrite the equation as:

cos^2A + cos^2C = 1

Substituting cosC = sinA, we get:

cos^2A + sin^2A = 1

Now, let's solve for cosA.

Solving for cosA

We know that tgA = 2√6. By definition, tgA = sinA/cosA. Therefore, we can write:

sinA/cosA = 2√6

To simplify the equation, we can square both sides:

(sinA/cosA)^2 = (2√6)^2

sin^2A/cos^2A = 24

Using the trigonometric identity sin^2A + cos^2A = 1, we can substitute sin^2A with 1 - cos^2A:

(1 - cos^2A)/cos^2A = 24

Now, let's solve for cos^2A.

Solving for cos^2A

To solve the equation (1 - cos^2A)/cos^2A = 24, we can multiply both sides by cos^2A to eliminate the denominator:

1 - cos^2A = 24 * cos^2A

Rearranging the equation, we get:

25 * cos^2A = 1

Dividing both sides by 25, we find:

cos^2A = 1/25

Taking the square root of both sides, we get:

cosA = ±1/5

Since cosA represents the ratio of the adjacent side to the hypotenuse in a right triangle, it cannot be negative. Therefore, the value of cosA is:

cosA = 1/5

Please let me know if you need any further assistance!