Understanding Trig Ratios in Right Triangles (Grades 11-12)

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Understanding Trig Ratios in Right Triangles

1. 
[math]Delta ABC[/math] is an acute triangle. The sine of angle A can be expressed as [math](BC)/(AC)[/math].
Equilateral Triangle ABC v1
  1. True
  2. False
2. 
In [math]Delta ABC[/math], [math]ang B[/math] is a right angle and [math]sin(C) = 0.829[/math]. If [math]Delta EFG \ ~ \ Delta ABC[/math], then [math]sin(G) = 0.829[/math].
  1. True
  2. False
3. 
Two right triangles both have angle measures of 25°, 65°, and 90°, but one triangle has side lengths which are double the lengths of the other triangle. Therefore, the sine of the smallest angle in each triangle will not be equal.
  1. True
  2. False
4. 
The ratio of the largest leg of a right triangle to its hypotenuse will ALWAYS have the same value for ANY two similar right triangles.
  1. True
  2. False
5. 
In [math]Delta ABC[/math], as seen below, [math]m ang C < m ang B[/math]. For any triangle that is similar to [math]Delta ABC[/math], the cosine of the smallest angle will be equal to [math](AC)/(BC)[/math].
Right Triangle ABC v2
  1. True
  2. False
6. 
[math]Delta ABC \ ~ \ Delta EFG[/math], and [math]ang B[/math] and [math]ang F[/math] are right angles. Which of the following is/are definitely true? Choose all correct answers.
  1. [math]cos(A) = cos(E)[/math]
  2. [math](BC)/(AC) = (FG)/(EG)[/math]
  3. [math]sin(A) = sin(E)[/math]
  4. [math](AB)/(AC) = (EF)/(EG)[/math]
7. 
[math]Delta ABC \ ~ \ Delta XYZ[/math], and [math]ang C[/math] and [math]ang Z[/math] are right angles. Which of the following is/are definitely true? There may be more than one correct answer.
  1. [math]sin(X) = (BC)/(AB)[/math]
  2. [math]tan(B) = (XZ)/(YZ)[/math]
  3. [math]cos(A) = (AC)/(XY)[/math]
  4. [math]tan(A) = (BC)/(XZ)[/math]
8. 
[math]Delta CDE \ ~ \ Delta HJK[/math], and [math]ang D[/math] and [math]ang J[/math] are right angles. Which of the following is/are definitely true? Choose all correct answers.
  1. [math]sin(E) = (CD)/(CE)[/math]
  2. [math]cos(E) = (DE)/(HK)[/math]
  3. [math]sin(K) = (CD)/(CE)[/math]
  4. [math]cos(K) = (DE)/(CE)[/math]
9. 
[math]Delta EGH \ ~ \ Delta LMN[/math], and [math]ang E[/math] and [math]ang L[/math] are right angles. Which of the following is/are definitely true? Choose all correct answers.
  1. [math]sin(G) = sin(M)[/math]
  2. [math]GH = MN[/math]
  3. [math]EH = LN[/math]
  4. [math](EH)/(GH) = (LN)/(MN)[/math]
10. 
[math]Delta ABC[/math] and [math]Delta QRS[/math] are both right triangles, where [math]ang B[/math] and [math]ang R[/math] are right angles. If [math]cos(C) = cos(S)[/math], which of the following is correct?
  1. [math]Delta ABC[/math] must be congruent to [math]Delta QRS[/math].
  2. [math]Delta ABC[/math] must be similar to [math]Delta QRS[/math].
  3. [math]Delta ABC[/math] and [math]Delta QRS[/math] may or may not be similar, but there's not enough information to be certain.
  4. [math]Delta ABC[/math] and [math]Delta QRS[/math] are not similar.

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