# 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.)