Question

In right AABC with the right angle at C, sin A = 7x – 2 and cos B = 5x + 6. Determine and state the value of x.

Answer 1

We have the next diagram

We have

`\sin (A)=(CB)/(AB)=7x-2`

then we have

`\cos (B)=(CB)/(AB)=5x+6`

because the trigonometric functions have the same ratio, we can do the next equality.

`7x-2=5x+6`

`7x-5x=6+2`

we sum similar terms

`2x=8`

we isolate the x

`x=(8)/(2)`

the value is x=4