In ΔHIJ, the measure of ∠J=90°, the measure of ∠H=15°, and JH = 54 feet. Find the length of HI to the nearest tenth of a foot
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Answer:
420 meters
Step-by-step explanation:
The first thing we must do is understand the exercise, the first thing is that they go in opposite directions, one goes clockwise and the other goes counter-clockwise.
We can interpret that one is in the "beginning" of the track and the other is in the "middle". Let's say that the length of the track is "x"
Now, their first meeting is when Amy has traveled 120 meters, which means that how Betty is in the middle would be x/2 - 120, which she traveled. We are told that Betty traveled 180 meters after that meeting point which means, how did she start "beginning" but that beginning can also be seen as the end, that is, distance x, traveled x - 180.
We can do the following proportion:
120*180 = (x/2 -120)*(x-180)
in resolving:
x^2-420*x+43200=43200
x^2 -420*x = 0
x*(x -420)=0
x - 420 = 0
x = 420
Therefore the circular track has a length of 420 meters