Question

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

Answer 1

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^-19/15.

Answer 2

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.

Answer 3

The answer of 31° is correct.

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

Tangent = opposite / adjacent

Answer 4

Determine the measure, to the nearest degree, of the smallest angle in a triangle with sides
of 4 m, 7 m, and 8 m. Sketch the triangle.