help with some homework please

Question

Find the acute angle α (in degrees) that satisfies the equation.

Answer 1

So this is a Trig question on one of the special triangles.

Note: It is to your advantage to become familiar with both the 30-60-90 and the 45-45-90 triangles, that way you will not have to memorize the whole unit circle.

If you make a 30-60-90 triangle, and pretend to stand at the 30° angle, when you look straight across you will intersect with the leg opposite the 30°, and that is where you will put a "1" for the leg length, moving counter clock wise, you will put a "2" for the hypotenuse leg and finally you will put a √3, for the adjacent (base) leg.

Cosine = (adjacent/hypotenuse), you are looking for (√3/2); you will quickly see the acute angle is the 30º angle.

Answer 2

∝ = 30°

Answer 3

Cosine of alpha is adjacent over hypotenuse.

So you can say √3 is the adjacent length and

2 is the hypotenuse length.

Using the Pythagorean theorem the reaming edge is length 1.

This is the same as a 30 60 90 triangle.

The original angle would be in the smallest angle spot or 30 degrees.

alpha is 30 degrees.