Question

The legs of a right triangle are lengths x and x√3. The cosine of the smallest angle of the triangle is _____.

Answer 1

Drawing a picture is always helpful:

Answer 2

The smallest angle will always be opposite the smallest side. Note that sqrt(3) is greater than 1 (sqrt(1) < sqrt(3)), so x * sqrt(3) is larger than x * 1. (x sqrt(1) < x sqrt*3) )

Answer 3

Now we have the angle to find. So, we only need to find the hypotenuse because
cos = adjacent / hypotenuse

We may use the Pythagorean theorem to find the hypotenuse, and then we simply take
\( \cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}} \)
For our cosine of the smallest angle. :)