In your exploration assignment, you used a trigonometric ratio to determine the various side lengths of a triangle. Use the following ratios to address the questions below:
a. $\footnotesize{\sin\theta = \frac{1}{2}}$
b. $\footnotesize{\sin\theta = \frac{6}{13}}$
c. $\footnotesize{\sin\theta = \frac{9}{10}}$
d. $\footnotesize{\sin\theta = \frac{12}{15}}$
e. $\footnotesize{\cos\theta = \frac{1}{2}}$
f. $\footnotesize{\cos\theta = \frac{6}{13}}$
g. $\footnotesize{\cos\theta = \frac{9}{10}}$
h. $\footnotesize{\cos\theta = \frac{12}{15}}$
i. $\footnotesize{\tan\theta = \frac{1}{2}}$
j. $\footnotesize{\tan\theta = \frac{6}{13}}$
k. $\footnotesize{\tan\theta = \frac{9}{10}}$
l. $\footnotesize{\tan\theta = \frac{12}{15}}$1. Use each trigonometric ratio to determine the length of all three sides of each triangle. Did you notice a pattern in the answers? If so, make sure you can explain the pattern.
2. Using similar triangles, calculate the altitude of each triangle. Round your answers to the nearest hundredth, if necessary.
3. In the Appendices folder in your course menu, there is a table of trigonometric values. If you know the trig ratio, you can calculate any angle. For example, for the trig ratio of
$\footnotesize{\sin\theta = \frac{2}{17}}$,
you can calculate the angle:
$\footnotesize{\sin\theta = \frac{2}{17}\approx 0.1176}$
The ratio $\footnotesize{\sin\theta \approx 0.1176}$ corresponds to an angle that measures somewhere between 6 and 7 degrees.
So, knowing this, use your trig tables to calculate the other angle measures of each non-right angle in the triangles described by the trig ratios above.
4. Before you come to the exploration meeting, make sure you know how to calculate the sine, cosine, and tangent of any angle between 0 and 90 using your calculator or other technology.
