Preview Activity 4.4.1.
Consider a right triangle that has one leg of length \(3\) and another leg of length \(\sqrt{3}\text{.}\) Let \(\theta\) be the angle that lies opposite the shorter leg.
(a)
Sketch a labeled picture of the triangle.
(b)
What is the exact length of the triangle’s hypotenuse?
(c)
What is the exact value of \(\sin(\theta)\text{?}\)
(d)
Rewrite your equation from (c) using the arcsine function in the form \(\arcsin(\Box) = \Delta\text{,}\) where \(\Box\) and \(\Delta\) are numerical values.
(e)
What special angle from the unit circle is \(\theta\text{?}\)
