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#1 2007-11-12 02:27:54

lisa123
Member
Registered: 2007-11-11
Posts: 5

need help!

A balloon is between two spotters who are 1.2 miles apart. One
>spotter reports that the angle of elevation of the balloon is 76
>degrees, and the other reports that it is 68 degrees. What is the
>altitude of the balloon in miles?

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#2 2007-11-12 04:04:40

TheDude
Member
Registered: 2007-10-23
Posts: 361

Re: need help!

Time to get familiar with one of my favorite laws, the Law of Sines.  First, we need to find the 3rd angle of the triangle formed by connecting the balloon and the two spotters.  Let's call spotter 1 point A, spotter 2 point B, and the balloon point C.  We know that angle BAC = 76 degrees and angle ABC = 68 degrees.  That means that angle ACB = 180 - (76 + 68) = 36 degrees.

Now, the Law of Sines states the for a triangle with angles A, B, C, and sides of length a, b, and c, where the side of length a is opposite of the angle A and similarly for the other 2, the following equation holds true:

Points A and B are 1.2 miles apart, which is equivalent to saying that side c is of length 1.2 miles.  Using the Law of Sines we can calculate that the length of side a is 1.98 miles and side b is 1.89 miles.  Now imagine a line going straight down from the balloon to the ground.  Call the length of this line x.  The value of x is the height of the balloon.  This is going to split the bottom of the triangle, side c, into 2 different lines.  Call the point where the vertical line and side c intersect point D.  We now have two new, right triangles: ACD and BCD.  What you want to do now is use the Pythagorean Theorem on both triangles to come up with a system of two equations and two variables and use them to solve for x.


Wrap it in bacon

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