If sin B=8/15 what is cos B

Question

In a right triangle <A and <B are acute 

Answer 1

If sin B=8/15

then sin B equals opposite over hypotenuse, the side opposite B is 8 and the hypotenuse is 15.

The adjacent side is x so x squared plus 8 squared equals 15 squared.

 

x squared plus 64 equals 225.  So x squared equals 225 minus 64 or 161.

 

x squared is 161 - x is the square root of 161

 

Cos B equals square root of 161 divided by 15.

 

Denny R 

Galion, OH

Answer 2

sinB=8/15 . use the identity sin²B+cos²B=1. 

So,cos²B=1-(8/15)²=(225-64)/225=169/225=(13/15)²

so, cosB=13/15 or -13/15.

Since B is acute angle cosB must be positive. So, cos B=13/15.