Tigonometry

Question

You have a right triangle with hypotenuse c and one of the acute angles at measure t. Using trigonometry, find c in terms of t. Also, after finding that, find the aproximate value of t that makes the hypotenuse as short as it can be. Restrict attention to values t that are less than 45 degrees. Explain method.

Answer 1

c^2 = a^2+ b^2 t = an acute angle 90-t = the other acute angle

c = a/sint = b/sin(90-t)

angle which makes c shortest is t = nearly Zero