Question #b66d2

1 Answer
Mar 28, 2017

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