# Lesson 2

Revisiting Right Triangles

• Let’s recall and use some things we know about right triangles.

### Problem 1

Which of the following is true?

A:

$$\sin(A) = \frac{6}{10}$$

B:

$$\cos(A) = \frac{6}{10}$$

C:

$$\sin(C) = \frac{6}{10}$$

D:

$$\cos(C) = \frac{8}{10}$$

### Problem 2

Here is triangle ABC:

1. Express the length of segment $$AB$$ using sine or cosine.
2. Express the length of segment $$BC$$ using sine or cosine.

### Problem 3

Triangle DEF is similar to triangle ABC.

1. What is the length of segment $$DE$$? What is the length of segment $$EF$$? Explain how you know.
2. Explain why the length of segment $$DE$$ is $$\cos(D)$$ and the length of segment $$EF$$ is $$\sin(D)$$.

### Problem 4

Here is a triangle.

Find $$\cos(A)$$, $$\sin(A)$$, and $$\tan(A)$$. Explain your reasoning.

### Problem 5

Sketch and label a right triangle $$ABC$$ with $$\tan(A) = 2$$.

### 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.

(From Unit 6, Lesson 1.)