Question

Question #b66d2

Answer 1

If we assume c is the unknown length of `sideC`

`sina = 9/18 = 0.5 = 30deg;sin60 = .866;`

`sideC = .866*18 = 15.6`in

Explanation:

The right triangle given has a hypotenuse of `18`in.

It has an opposite of `9`in.

From these we can find the sine of the angle we will call `a` which is across the triangle from it, or opposite to it.

There is a famous formula: `sina = (opp)/(hyp)`

Here, `sina = 9/18 = 0.5`

An angle with `sin=0.5` is `30deg`, which will fit into our triangle because we can see the angle across from our opposite is acute.

Now we know the three angles of the triangle add up to `180deg` so the remaining angle is `180 - 90 - 30 = 60deg`

We can find that `sin60deg = 0.866`

`sin60deg = 0.866 = (opp)/(hyp) = C/(hyp) = C/18`

`C = .866*18 = 15.6`in

So the unknown `sideC` of the triangle is `0.866*18=15.6`in