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.
I feel most confident about using trigonometric ratios to find unknown side lengths. I find it relatively straightforward to use sine, cosine, and tangent ratios to determine unknown side lengths in right triangles. I have practiced solving various problems using trigonometric ratios, which has boosted my confidence in this topic.
The most challenging topic for me in this unit has been solving problems that involve angles of elevation and depression. I find it difficult to visualize these situations accurately and understand the relationship between the angles and the sides of the right triangle. Determining which trigonometric ratio to use and applying it correctly in these problems is a bit tricky for me.
The Pythagorean Theorem can be used in various real-life scenarios. For example, it can be applied in construction projects to ensure that corners are square. By measuring the lengths of two sides of the right angle, we can calculate the length of the third side using the Pythagorean Theorem. This helps to ensure that structures are built accurately and without any leaning or imbalance. Additionally, the theorem can be used in navigation to determine distances. For instance, if a ship travels a certain distance east and then a certain distance north or south, we can apply the Pythagorean Theorem to calculate the direct distance between the starting and ending points.