Posted by **Hanna** on Monday, February 27, 2012 at 9:35pm.

To the nearest degree, what is the measure of the smallest angle of a right triangle whose legs measure 9 and 15?

- Geometry -
**MathMate**, Monday, February 27, 2012 at 10:13pm
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.

- Geometry -
**Hanna**, Monday, February 27, 2012 at 10:14pm
Tangent= Opposite/Hypotenuse

Tan 9/15=30.96 (This is the Smallest Angle)

Check:

90(This is the Right angle)+30.96=120.9

180-120.9=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.

- Geometry -
**MathMate**, Tuesday, February 28, 2012 at 7:23am
The answer of 31° is correct.

Your definition of tangent was probably a typo, and it should read:

Tangent = opposite / adjacent

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