Step by step
The question
Question: find cos B.
A and B are the small angles of a right triangle, and sin A = 4/5.
1 Draw the triangle
A and B are the two small angles of one right triangle.
We draw it: A at the bottom, B at the top.
2 Name the sides from each angle
Look at side a.
From A, it is across: the opposite side.
We write opp, adj and hyp for short.
From B, the same side a is next to it: the adjacent side.
Side c is the hypotenuse for both angles.
sin is the opposite side over the hypotenuse.
From A: a over c.
cos is the adjacent side over the hypotenuse.
From B: a/c too.
Careful!
B is the other angle.
The side next to B is the side across from A.
Same two sides, same fraction.
So cos B = sin A.
3 Find cos B
sin A is 4/5.
So cos B = 4/5 too.
4 Check
Let's check with the calculator.
The sin⁻¹ button turns sin A back into the angle: A is about 53.1°.
So B is 90 minus 53.1: 36.9°.
cos 36.9° is about 0.8.
That is 4/5 again: 4 divided by 5 is 0.8.
So cos B = 4/5 is right!
Let's look back.
First: draw the triangle.
Then: name the sides from each angle.
Then: find cos B.
Last: check.