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Question 1027630: http://prntscr.com/an0h5g
Out of curiosity, why can't cosine be used to solve this?
Why can't the hypotenuse be used to figure out how tall the shorter building is?
Found 3 solutions by Edwin McCravy, josgarithmetic, MathTherapy:
Answer by Edwin McCravy(20059)   (Show Source):
You can put this solution on YOUR website!
You can't use the cosine or the sine because they involve
the hypotenuse. You neither know the hypotenuse nor is
the hypotenuse the side that you want to find.
You know the angle and the adjacent side only, and you want
to find the opposite x. So you use whichever one of the three
main trig ratios that has both the side given 51m and the side
you want to find as a numerator and denominator. That is the
tangent because tangent = opposite/adjacent.
Again, always pick the trig ratio that has both the known side
and the side you want to find as a numerator and denominator.
Edwin
Answer by josgarithmetic(39620)  (Show Source):
You can put this solution on YOUR website! Consider the main triangle near the upper neighborhood between the two buildings. Legs of 51, and y, and the acute angle of this right triangle is 15 degrees.
The hypotenuse is unknown, and one of the legs, y, is unknown. You could set up a relationship using cosine if you want. Go ahead!
r for the hypotenuse which you do not yet know.
 ----NOT BAD, is it? You picked well, and you know you can now find r, the hypotenuse; BUT YOU DO NOT NEED THE HYPOTENUSE!!!
Let's continue on, your way.
so now you have a value for the hypotenuse, r. You really now CAN use Pythagorean Theorem to get y.
 , everything computable; compute this and then use it for finding how tall the shorter building is.
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website!
http://prntscr.com/an0h5g
Out of curiosity, why can't cosine be used to solve this?
Why can't the hypotenuse be used to figure out how tall the shorter building is?
You’re looking to find the upper section of the taller building, so you can subtract that section from the taller building’s
height to get the shorter building’s height. The only way to obtain that is to use given measurements, such as the angle of depression
( ) and base side of the right triangle that’s formed. As the angle of depression is given, the base side (51 m) represents
the ADJACENT leg, and the OPPOSITE leg (upper section of taller building’s height) is being sought,  .
Assuming that you’d want to use cosine, why would you knowing that cosine involves the hypotenuse when the hypotenuse is not part
of the problem at all? Remember, the hypotenuse is neither given nor is it being sought.
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