SOLUTION: If I have a measurement of a right triangle where the bottom measures 30 and there are two missing signs and the beta is given which measures 29 degrees 45 minutes and 39 seconds w
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Question 459670: If I have a measurement of a right triangle where the bottom measures 30 and there are two missing signs and the beta is given which measures 29 degrees 45 minutes and 39 seconds what is the alpha and the other two measurements of the triangle?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Two missing signs? Since when does a triangle of any kind have signs? And how is your triangle oriented? Is the hypotenuse on the "bottom"? Or is the "bottom" one of the legs? In any triangle, the sum of the angles is 180 degrees. In a right triangle, one of the angles measures 90 degrees by definition, hence the sum of the other two angles must be 90 degrees. So if you are given the measure of one of the acute angles, subtract that measure from 90 to get the measure of the other angle.
If you are given the measure of the hypotenuse, then the sine function of one of the acute angles times the hypotenuse is the measure of the side opposite of the angle.
If you are given one of the legs, then the cosecant of the angle opposite the given leg times the measure of the given leg is the measure of the hypotenuse.
Either way, once you have the hypotenuse and one side, you can use Pythagoras to get the remaining side.
John
My calculator said it, I believe it, that settles it
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