CPM Homework Help : INT2 Problem 12-63

A $30°$ - $60°$ - $90°$ triangle has a hypotenuse of length $2$ units. Sketch and label the triangle, including the length of each side. Then use your diagram to determine exact values for the following trig expressions.

Hint:

Right triangle labeled as follows: horizontal leg, x times the square root of 3, vertical leg, x, hypotenuse, 2, x, angle opposite horizontal leg, 60 degrees, angle opposite vertical leg, 30 degrees.

Compute without a calculator

$\text{tan }30°$

$\text{sin }30°$

$\text{cos }30°$

How is $\text{sin }60°$ related to $\text{cos }30°$ ? Is the relationship true for any pair of acute angles in a right triangle? Explain your reasoning.