Question

If sinA=.15, cosB = x - .86, and A+B=90 degrees...what is the value of x?

Answer 1

Answer:

90.71

Step-by-step explanation:

You equal both A+B to 90

.15+x-.86= 90

x-0.71=90

90.71=x

Answer 2

Given : sin A=0.15, cos B=x-0.86 and A+B=90 degree=$\frac{\pi}{2}$

To find : the value of x.

Step-by-step explanation:

We know that,

sin(A+B)=sinA cosB+cosA sinB$\hfill (1)$

cos(A+B)=cosA cosB-sinA sinB$\hfill (2)$

Consider (1),

sin(A+B)=sinA cosB+cosA sinB

$\implies$sin $\frac{\pi}{2}$=0.15(x-0.86)+cosA sinB

$\implies$0.15x-0.129+cosA sinB=1$\hfill (3)$

and from (2),

cos(A+B)=cosA cosB-sinA sinB

$\implies$ cos$\frac{\pi}{2}$=cosA (x-0.86)-0.15 sinB

$\implies$ cosA (x-0.86)-0.15 sinB

$\implies$ sinB=$\frac{x-0.86}{0.15}$cosA

substitute in (3),

0.15x-0.129+($\frac{x-0.86}{0.15}$ )(1-(0.15)^2)=0

$\implies$0.0225x-0.01935+x-0.86-0.0225x+0.01935=0

$\implies$x=0.86

The value of x is 0.86.