Geometry
posted by Hanna on .
To the nearest degree, what is the measure of the smallest angle of a right triangle whose legs measure 9 and 15?

There are two acute angles in a right triangle. The tangents of these angles are the ratio of the legs. The small ratio corresponds to the smaller angle.
You'd be looking for tan^{1}9/15. 
Tangent= Opposite/Hypotenuse
Tan 9/15=30.96 (This is the Smallest Angle)
Check:
90(This is the Right angle)+30.96=120.9
180120.9=59.1(This is the third angle.)
9/sin 30.96 = 15/sin 59.1.
This Does Work.
So the Smallest Angle is 30.9 Degrees, rounded to 31. 
The answer of 31° is correct.
Your definition of tangent was probably a typo, and it should read:
Tangent = opposite / adjacent