Question

Please help!!

In right angle abc C = 90, if sin A=m, find cos B


the answer options are:

•90-m
•90+m
•45-m
• m

Answer 1

In a right triangle, the cosine of one acute angle is equal to the sine of the other. Therefore, if sin A = m, then cos B is also equal to m.

Step-by-step explanation:

In right triangle ABC with angle C being 90 degrees, if sin A is equal to m, we want to find cos B. Because triangle ABC is a right triangle, we can apply the fact that in a right triangle, the sum of the squares of the two legs is equal to the square of the hypotenuse (Pythagorean theorem), and the angles other than the right angle must sum to 90 degrees.

Since A and B are the acute angles, A + B = 90 degrees. If sin A = m, using the basic trigonometric identity sin A = cos(90 degrees - A), we can deduce that cos B = cos(90 degrees - A) = sin A = m. Therefore, cos B = m.