Nancy explains how to solve a right triangle by finding missing sides and angles. She emphasizes using trig functions (sine, cosine, tangent) and the Pythagorean theorem. She demonstrates solving for missing sides 'a' and 'c' and finding angle 'B' in a given triangle. She also mentions variations in triangle orientations and offers tips for approaching different scenarios in trigonometry.
Here are the key facts extracted from the text:
1. The speaker's name is Nancy.
2. The topic is solving a right triangle by finding missing sides and angles.
3. Special right triangles, like 30-60-90 or 45-45-90, are not discussed.
4. Trig functions like sine, cosine, and tangent are introduced.
5. The trigonometric relationships SOH-CAH-TOA are explained.
6. The terms "opposite," "adjacent," and "hypotenuse" are defined.
7. To find a missing side, pick the trig function that involves the known side and the one you're looking for.
8. The tangent function is used to find a missing side.
9. An equation, tan(34 degrees) = a/8, is used to find the value of side 'a.'
10. To solve for 'a,' you multiply both sides by 8.
11. 'a' is approximately 5.4 units long.
12. To find another missing side, the cosine function is used.
13. An equation, cos(34 degrees) = 8/c, is used to find the value of side 'c.'
14. To solve for 'c,' you multiply both sides by 'c.'
15. 'c' is approximately 9.6 units long.
16. The Pythagorean theorem (a² + b² = c²) is introduced as an alternative method.
17. Using the Pythagorean theorem, 'c' is again found to be approximately 9.6 units long.
18. The last step is finding the unlabeled angle 'B.'
19. All three angles in a triangle add up to 180 degrees, so angle 'B' is found to be 56 degrees.
These facts summarize the key information from the text, excluding opinions or explanations.