Question

В треугольнике ABC угол C равен 90, cos A=(корень из 7)/4Найдите sin A

Answer 1

SinA=корень(1-cosA в квадрате)=корень(1-7/16)=корень((16-7)/16)=корень(9/16)=3/4

Answer 2

Решение:

Given: - Triangle ABC with a right angle at C - cos(A) = √7/4

We need to find sin(A).

Using the trigonometric identity sin^2(A) + cos^2(A) = 1, we can solve for sin(A).

We know that cos^2(A) + sin^2(A) = 1.

Substitute the given value of cos(A) into the equation:

(√7/4)^2 + sin^2(A) = 1 7/16 + sin^2(A) = 1 sin^2(A) = 1 - 7/16 sin^2(A) = 9/16

Taking the square root of both sides to solve for sin(A):

sin(A) = ±√(9/16) sin(A) = ±(3/4)

Since we're dealing with a triangle, and in this context, the sine function represents the length of the side opposite the angle A divided by the length of the hypotenuse, we can conclude that sin(A) = 3/4.

So, sin(A) = 3/4.