Question #b66d2

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Answer 1 · 2017-03-28T05:21:38

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

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

$sideC = .866*18 = 15.6$ in

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