Lesson 2

Revisiting Right Triangles

Problem 1

Which of the following is true?

Right triangle. A, B C, Right angle B. Side A, B length 8, side C B length 6, side A, C length 10.
A:

\(\sin(A) = \frac{6}{10}\)

B:

\(\cos(A) = \frac{6}{10}\)

C:

\(\sin(B) = \frac{8}{10}\)

D:

\(\cos(B) = \frac{6}{10}\)

Solution

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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.
Right triangle. A, B C, Right angle B. Side A, C length 1. Angle A measure theta.

Solution

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Problem 3

Triangle DEF is similar to triangle ABC.

Two triangles. First, A, B C with B is a right angle. Side A, B length 12, side B C length 5, side A, C length 13. Second, D E F, E is a right angle, side D F length 1.
  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 \(\sin(D)\).

Solution

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Problem 4

Here is a triangle.

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

Triangle A, B C. Angle C is a right angle. Side A, C length 6. Side B C length 2.

Solution

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Problem 5

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

A blank coordinate plane, x, 0 to 2 by 1, y, 0 to 3 by 1.

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.)