Step by step
The question
Question: find sin B.
A and B are the small angles of a right triangle, and cos A = 0.6.
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 b.
From A, it is next to it: the adjacent side.
We write opp, adj and hyp for short.
From B, the same side b is across: the opposite side.
Side c is the hypotenuse for both angles.
cos is the adjacent side over the hypotenuse.
From A: b over c.
sin is the opposite side over the hypotenuse.
From B: b/c too.
Careful!
B is the other angle.
The side across from B is the side next to A.
Same two sides, same fraction.
So sin B = cos A.
3 Find sin B
cos A is 0.6.
So sin B = 0.6 too.
4 Check
Let's check with the calculator.
The cos⁻¹ button turns cos A back into the angle: A is about 53.1°.
So B is 90 minus 53.1: 36.9°.
sin 36.9° is about 0.6.
That is 0.6 again.
So sin B = 0.6 is right!
Let's look back.
First: draw the triangle.
Then: name the sides from each angle.
Then: find sin B.
Last: check.