Activity 4.1.3.
In each of the following scenarios involving a right triangle, determine the exact values of as many of the remaining side lengths and angle measures (in radians) that you can. If there are quantities that you cannot determine, explain why. For every prompt, draw a labeled diagram of the situation.
(a)
A right triangle with hypotenuse \(7\) and one non-right angle of measure \(\frac{\pi}{7}\text{.}\)
(b)
A right triangle with non-right angle \(\alpha\) that satisfies \(\sin(\alpha) = \frac{3}{5}\text{.}\)
(c)
A right triangle where one of the non-right angles has measure \(1.2\) and the hypotenuse has length \(2.7\text{.}\)
(d)
(e)
(f)
A right triangle where one of the non-right angles has measure \(\frac{\pi}{5}\) and the leg opposite this angle has length \(4\text{.}\)
