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Right Triangle Kite Problem

Date: 01/16/97 at 16:09:29
From: Alvin Wilson
Subject: How high is the kite?

Hello Dr. Math,

I am having trouble with a trigometry 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?

Alvin Wilson 

Date: 01/16/97 at 18:32:22
From: Doctor Scott
Subject: Re: How high is the kite?

Hey Alvin!!

Great question.  It's a good example of a right triangle trigonometry 
problem.  Remember that in a right triangle, ABC, with a right angle 
at B,

                  |  \
                  |    \
                  |      \
                  |        \
                  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)

-Doctor Scott,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/   
Associated Topics:
High School Trigonometry

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