In a right-angled triangle, angle C = 90 degrees, find the value of the cosine of angle A if the sine of angle B is 4/5.

1) The value of the cosine of the angle cos A can be determined immediately, given that <A + <B = 90 ° according to the following formula for the angles of a right-angled triangle:

cos A = sin (90 – A) = sin B = 4/5.

2) Let’s check and calculate it in another way, writing out the values of the sine and cosine through the sides in the triangle, legs a and b, hypotenuse c.

cos A = b / c; sin A = a / c; sin B = b / c; cos B = a / c.

Having considered the formulas, we write down that: cos A = sin B = b / c = 4/5.

Answer: cos A = 4/5.