#What is the value of x?

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#A. 4#

#B. 4sqrt3#

#C. 8#

#D. 8sqrt3#

1 Answer
May 26, 2017

#4sqrt(3) = x#, or B

Explanation:

In this one we know the angle and the hypotenuse, but we don't know the opposite side. So we need something to relate opposite to hypotenuse when given a certain angle.

#sin(theta) = "opposite"/"hypotenuse"# Works well here.

In this case we need to plug everything in as we see it. #theta# is 60 degrees, opposite is the opposite leg from the angle or #x#, and hypotenuse is the longest side to the triangle or 8 in this case.
So:

#sin(60) = x/8# Multiply 8 on both sides to isolate #x#
#color(red)(8)sin(60) = (x*color(red)(8))/8#
#8sin(60) = x# Now we just evaluate to get what x is equal to
#(8sqrt(3))/2 = x#
#4sqrt(3) = x#

So B is the answer