Question

В треугольнике авс угол с равен 90 ав=3 cosA=2корня из 2 деленное на 3, найдите ВС

Answer 1

sinA = ВС/АВ

ВС=sinA*AB

ВС=2 КОРНЯ ИЗ 2 *3

BC=6 КОРНЕЙ ИЗ 2

Answer 2

Solving for BC in Triangle ABC

To solve for BC in triangle ABC, we can use the given information that angle A is 90 degrees and cos(A) = 2√2/3.

Given: - Angle A = 90 degrees - cos(A) = 2√2/3

Using Trigonometric Identities to Find BC

We can use the trigonometric identity cos^2(A) + sin^2(A) = 1 to find sin(A) and then use the sine ratio to find BC.

From the given information, we have: - cos(A) = 2√2/3

Using the identity cos^2(A) + sin^2(A) = 1, we can solve for sin(A): - sin^2(A) = 1 - cos^2(A) - sin^2(A) = 1 - (2√2/3)^2 - sin^2(A) = 1 - 8/9 - sin^2(A) = 1/9 - sin(A) = ±1/3

Since angle A is in the first quadrant (0 to 90 degrees), sin(A) is positive: - sin(A) = 1/3

Now, we can use the sine ratio to find BC: - sin(A) = opposite/hypotenuse - 1/3 = BC/AC

Calculating BC

We need to find the length of BC. To do this, we need to find the length of AC.

Unfortunately, the given information does not include the length of AC or any other side lengths. Without this information, it is not possible to calculate the exact length of BC.

If you have the length of AC or additional information about the triangle, please provide it so that we can proceed with the calculation.