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Right Triangle Kite Problem

When flying a kite, 150 ft. makes an an angle of 51 degrees with the 
ground. Assume the string is straight. How high above the ground is 
the kite to the nearest tenth of a foot?




Remember that in a right triangle, ABC, with a right angle 
at B,

                  A
                  |\
                  |  \
                  |    \
                  |      \
                  |        \
                  |__________\
                  B           C


 the sine of angle C is defined to be OPPOSITE / HYPOTENUSE  (AB/AC)
 the cosine of C is define d to be ADJACENT / HYPOTENUSE  (BC/AC)
 the tangent of C is defined to be OPPOSITE / ADJACENT  (AB/BC)

It's usually a good idea to "zone in" on an angle, then decide 
what trig ratio to use. So, for your problem, the HYPOTENUSE is 
the length of kite string (150) and the angle with the ground is 
at C (51 degrees).  So, we are looking for side BA.  

With the angle in mind, we are trying to FIND the opposite side 
and we are given the hypotenuse, so we think SINE!

So,   sin 51 = AB / 150.   

Using a calculator or table, sin 51 = 0.77714596, so we have

   0.77714596    =   AB
 --------------     -----
        1            150


We can solve this by cross multiplying: 150*0.7714596 = AB
                                     
So, AB = 116.6  (rounded to the nearest tenth)