Phoebe and Tucker are 48m apart. Phoebe looks up at an angle of 43 degrees to see a hot air balloon hovering in the sky directly between her and Tucker. Tucker looks up at an angle of 31 degrees to see the hot air balloon.
A.) Explain how it could be determined who is closer to the balloon without doing any calculations.
phoube
To determine who is closer to the hot air balloon without doing any calculations, we can analyze the given information and use some basic logic.
From the given information, we know that Phoebe and Tucker are both looking up at the hot air balloon, which is hovering directly between them.
Phoebe's angle of elevation (43 degrees) is greater than Tucker's angle of elevation (31 degrees). This means that Phoebe has to look up at a steeper angle to see the same object in the sky.
In general, when two people are looking at the same object and one has to tilt their head more to see it, that person is usually closer to the object.
Therefore, based on the information given, we can assume that Tucker is closer to the hot air balloon than Phoebe.
I suggest you to do a diagram to guide yourself.
Draw a line and let the points at the end to be Phoebe and Tucker locations.
Then with help of a protactor, draw the line whether the angle is formed.
Check by yourself who is closer, or try it on real life, see an object and imagine the angle formed, then go closer and imagine again the angle.