Recall: gives the length of the vertical side of the "Master Right Triangle" at angle and is the length of the horizontal side of the "Master Right Triangle" at the angle .

Master Right Triangle

Task 1

On your paper, compute the ratio of the side opposite the angle to the hypotenuse as a decimal.

Task 2

With the "Master Right Triangle," make a triangle approximately similar to the triangle in Task 1 and compute the ratio of the side opposite the angle to the hypotenuse, which we have referred to as . How does this ratio compare to your ratio in Task 1?

Task 3

Is the triangle below similar to the triangle from Task 1? If yes, what do you think the ratio of the opposite side to the hypotenuse will be? Calculate it and check. If no, explain why it is not similar.

Task 4

With your calculator, compute . How does that compare to your previously computed ratios? How does it compare to ?

Task 5

Do you have a conjecture about and ? Try to justify your conjecture (Remember SOH CAH TOA and the definition of ).

Task 6

Compute and . How do they compare? Do you have a conjecture about and ? Try to justify your conjecture (Remember SOH CAH TOA and the definition of ).

Task 7

Using the Pythagorean Theorem, find a way to relate and . Can you find a similar way to relate and ?