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.
The topic I feel the most confident about in this unit is using trigonometric ratios to find unknown side lengths. I feel confident in this topic because I understand how to set up and solve trigonometric equations to find missing side lengths in right triangles. I also find it satisfying to use sine, cosine, and tangent ratios to solve problems involving missing side lengths.
The most challenging topic for me in this unit has been solving problems that involve angles of elevation and depression. I find these problems challenging because they often involve setting up equations using multiple trigonometric ratios and variables, which can be confusing to keep track of. Additionally, visualizing these scenarios and accurately determining which trigonometric ratio to use can be difficult for me.
One scenario where the Pythagorean Theorem could be used in real life is in construction. For example, when building a house, the Pythagorean Theorem can be used to ensure that the foundation of the house is square. By measuring the length and width of the foundation and using the Pythagorean Theorem to calculate the diagonal distance between two corners, builders can make sure that the house is built at right angles and is structurally sound. This application of the Pythagorean Theorem helps ensure the stability and integrity of the structure being built.