Question

Can someone help me solve for this expression?

Answer 1

We require the law of sines here: `SinC*a=h`

Explanation:

The law for this particular one would be:
`a/sin(90)=h/sinC`
Now the sin of 90 is 1, so therefore:
`a=h/sinC`
`SinC*a=h`
The answer you have picked should be correct

Answer 2

You selected the right answer; it's `asinC`.

Explanation:

We can try all the answers out.

We can simplify all the answers and find the right one by using `"SOH CAH TOA"`:

`sin="opposite"/"hypotenuse"`

`cos="adjacent"/"hypotenuse"`

`tan="opposite"/"adjacent"`

The first option is `csinB`. Since `angle B` isn't a part of the right triangle, we can't actually compute it in terms of the lengths in question, so this answer is probably wrong.

The next option is `asinC`. `sinC` is the opposite side of `C` divided by the hypotenuse of that triangle. That would be `h/a`. Multiplying this value by `a` gets `a*h/a` or just `h`. Since this is what the question was asking for, that's the right answer. Let's check the rest anyway:

The third option is `bsinC`. We know from before that `sinC` is `h/a`. Multiplying this by `b` gets `b*h/a`, which can't be simplified. This isn't the height of the triangle, so this isn't the right answer.

The last option is `asinB`. We know from before that we can't actually compute `sinB`, so this answer is also wrong.

That means the correct answer `asinC`.