You have learned about the following topics:
using the Pythagorean Theorem and its converse
using properties of special right triangles (45˚–45˚–90˚ and 30˚–60˚–90˚)
using trigonometric ratios to find unknown side lengths
using trigonometric ratios to find unknown angle measures
solving problems that involves angles of elevation and depression
Reflect on each of these topics and answer two of the following questions:
Which topic in this unit do you feel the most confident about and why?
Which topic in this unit has been the most challenging for you and why?
Describe a scenario where the Pythagorean Theorem could be used in real life
Post in the discussion with answers to these questions. Next, view posts from your classmates and respond to two of them. Do you feel confident about the same topic as your classmates? Why does this topic make sense to you? Do you share the same challenge as your classmates? If so, what can you do to overcome that challenge? Do you understand the examples your classmates provided of using the Pythagorean Theorem in real life? Do their examples apply to your life?
I feel the most confident about using trigonometric ratios to find unknown side lengths. I have practiced a lot of problems involving sine, cosine, and tangent functions, so I feel comfortable using them to solve for missing sides in right triangles. I also understand how to set up and use the ratios correctly, which helps me approach problems with more ease.
The most challenging topic for me in this unit has been solving problems that involve angles of elevation and depression. I sometimes struggle with visualizing the situation and determining which trigonometric ratio to use. Additionally, setting up the equation correctly can be tricky, as I need to consider the relationship between the angle of elevation or depression and the side lengths of the triangle.
One scenario where the Pythagorean Theorem could be used in real life is when constructing a fence for a garden. By using the Pythagorean Theorem, you can calculate the diagonal length of the garden to ensure that the fence will reach from one corner to the next. This helps ensure that the fence will completely enclose the garden area without leaving any gaps.
Overall, I feel confident about trigonometric ratios, but I could use some more practice with solving problems involving angles of elevation and depression. It's helpful to see how my classmates have applied the Pythagorean Theorem in real life, as it helps me understand the practical applications of the concept. By practicing more problems and seeking clarification from my teacher, I can continue to improve in this area.