SOLUTION: to the nearest tenth of a degree, find the sizes of the acute angles in the right triangle whose hypotenuse is 2.5 times as long as its short leg.

Question 148271: to the nearest tenth of a degree, find the sizes of the acute angles in the right triangle whose hypotenuse is 2.5 times as long as its short leg.
Found 2 solutions by vleith, Nate:
Answer by vleith(2983) (Show Source): You can put this solution on YOUR website!
Assume the short side is adjacent to the hypotenuse.
cos(z) = adjacent/hypotenuse = 1/2.5
To find z, use arccosine(1/2.5) = z = 23.6
So one angle is 23.6 degrees and the other one is 180-90-23.6 = 66.4degrees
Answer by Nate(3500) (Show Source): You can put this solution on YOUR website!

Let's begin with angle O. We need a trig identity that would include the opposite leg and the hypotenuse. _SOH_ CAH TOA
sin O = x / 2.5x
sin O = 1 / 2.5
sin O = 0.4
O = 23.6 degrees
Angle Q = 90 - Angle O
Angle Q = 90 - 23.6
Angle Q = 66.4 degrees
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