Question

In right triangle ABC with the right angle at C, sin A= 2x + .1 and cos B = 4x - .7. Determine and state the vaule of x.

Answer 1

Imagine $\angle A$ at the top of the triangle and $\angle B$ at the bottom. (or used the attached picture for reference)

$\sin A= \frac{opposite}{hypotenuse}$

$\cos B = \frac{adjacent}{hypotenuse}$

One thing to note, however, is that the side opposite $\angle A$ is the same side as the one adjacent to $\angle B$! Thus $\sin A=\cos B$.

Substitute these values for $2x+0.1$ and $4x-0.7$ and solve.

 $4x-0.7=2x+0.1 \\ 4x=2x+0.8 \\ 2x=0.8\\ \boxed{x=0.4}$