SOLUTION: could i find the two missing side lengths of a right triangle if i only know one side length and one angle measure?

Question 566431: could i find the two missing side lengths of a right triangle if i only know one side length and one angle measure?
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
I see three cases:
1) If the angle measure you have is 90 degrees, it only tells you that the triangle is a right triangle. There's nothing you can do with the information given.
2 and 3) If you know the measure of an acute angle in a right triangle, you know the measure of all three angles. That is so because you know that there is a 90 degree angle, and you can calculate the measure of the third angle by difference.
2) If you also know the length of one side, and you know what angle is opposite that side, then you can find the two missing sides.
3) If you know the length of one side, but you do not know what angle is opposite that side, you have 3 possibilities.
EXAMPLE:
If you tell me that your right triangle has an angle measuring 36.87 degrees and a side measuring 60 mm, I know from the angle and trigonometric functions, that the sides' lengths are in the ratio 3:4:5, with the shorter side opposite the smaller, given angle, and the longer side opposite the right angle.
If I knew that the 60 mm side is the longest one, I would know that the side lengths are 36, 48, and 60 mm.
If I knew that the shorter side measures 60 mm, I would know that the side lengths are 60, 80, and 100 mm.
If the medium length side is 60 mm long, the side lengths are 45, 60 and 75mm.
If I don't know which one is the side that is 60 mm long, I can only say that your triangle is one of those three.
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