snow harness
Please help. I cannot figure out how to solve this lol. I cannot figure out how to determine if the angle is being bisected and if it is a right angle. Even if I could, I'm not sure how to use that information to make an inequality. Also, my class hasn't gotten to trig yet, so I know there is something relatively simple that I am missing. Any help is appreciated.
real sphinxBOT
pulsar gull
I don't blame you for struggling, because the question is bad. There is still something to be learned, though!
A triangle consists of three side lengths and three angles (you knew that, of course). If we know none of these six values, then we can't determine the triangle's size and shape. The fewest number of values that we need to be given to determine its size and shape is three values (although sometimes we need more values). In the top triangle in the picture, for instance, we're given two side lengths (the upright 15 and the 20) and one angle (the 48⁰ angle).
If we're given just the right combination of three values (there are four such combinations), then we can actually calculate all three of the others, thereby determining the size and shape of the triangle completely. It just so happens that we are given such a "just right" combination of three values for the top triangle. This means that the length of the shared side can have only one possible value, which, if we combine it with the 15 and 17 that we're given for the bottom triangle, completely determines the bottom triangle also!
All that to say: The unknown angle can only have one value, because both triangles' size and shape are fully determined. (You can tell your teacher this if they ask why the question is bad.)