Question

I’m confused on this one

Answer 1

Y would equal 6.16.

We can use trigonometry and label AC as the hypotenuse and BC as the adjacent side.

This means we have to use the cosine ratio, cos = Adjacent/hypotenuse, and so to find the adjacent we must do cos(44.25) × 8.6, which is 6.16.

I hope this helps!

Answer 2

The answer is

First of all, note that we can solve all angles, since we have

$\hat{A}+\hat{B}+\hat{C} = 180 \iff \hat{A}+90+44.25 = 180 \iff \hat{A} = 180-90-44.25 = 45.75$

where $\hat{A}$ is the angle centered in vertex A, and so on.

Now we can use the law of sines, which states that the ratio between a side and the sine of the opposite angles is constant.

So, you would have

$\frac{AC}{\sin(\hat{B})} = \frac{BC}{\sin(\hat{A})}$

plug in the known values:

$\frac{8.6}{\sin(90)} = \frac{BC}{\sin(45.75)}$

Since sin(90)=1, the denominator of the first fraction disappears. Finally, we can solve for BC:

$BC = 8.6 \cdot \sin(45.75) \approx 8.4338\ldots$

Which gives 8.43 when rounded as required.