Lesson 2
Revisiting Right Triangles
Problem 1
Which of the following is true?
\(\sin(A) = \frac{6}{10}\)
\(\cos(A) = \frac{6}{10}\)
\(\sin(C) = \frac{6}{10}\)
\(\cos(C) = \frac{8}{10}\)
Solution
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Problem 2
Here is triangle ABC:
- Express the length of segment \(AB\) using sine or cosine.
- Express the length of segment \(BC\) using sine or cosine.
Solution
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Problem 3
Triangle DEF is similar to triangle ABC.
- What is the length of segment \(DE\)? What is the length of segment \(EF\)? Explain how you know.
- Explain why the length of segment \(DE\) is \(\cos(D)\) and the length of segment \(EF\) is \(\sin(D)\).
Solution
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Problem 4
Here is a triangle.
Find \(\cos(A)\), \(\sin(A)\), and \(\tan(A)\). Explain your reasoning.
Solution
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Problem 5
Sketch and label a right triangle \(ABC\) with \(\tan(A) = 2\).
Solution
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Problem 6
The point \((1,4)\) lies on a circle with center \((0,0)\). Name at least one point in each quadrant that lies on the circle.
Solution
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(From Unit 6, Lesson 1.)