Question

Which equation could be used to find the height of the flagpole

Answer 1

X = height of pole (in meters)

With respect to the 50 degree angle, the side x is the opposite leg. It is the leg furthest from the reference angle. The hypotenuse is 5 meters. 

The trig function sine ties together the opposite and hypotenuse

sin(angle) = opposite/hypotenuse
sin(50) = x/5
5*sin(50) = x .... multiply both sides by 5
x = 5*sin(50)

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Since x = 5*sin(50) isn't listed as an answer choice, let's try using cosine. We can't use it right away because we don't know the adjacent side. What we can do is change the reference angle. The missing angle of the triangle is 90-50 = 40 degrees. Let's make the 40 degree angle the reference angle

So x is now the adjacent side with respect to the 40 degree reference angle. The hypotenuse is always the longest side. The hypotenuse stays at 5.

cos(angle) = adjacent/hypotenuse
cos(40) = x/5
5*cos(40) = x
x = 5*cos(40)

This expression is listed. The answer is choice B