Trig Ratios and Special Triangles (Grades 11-12)

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Trig Ratios and Special Triangles

1. 
For triangle ABC, if [math]tan(B) = 1/sqrt(3)[/math], then its angle measures are either [math]30°-60°-90°[/math] or [math]45°-45°-90°.[/math]
Right Triangle ABC v1
  1. True
  2. False
2. 
For triangle [math]ABC[/math], [math]cos(B) = 1/sqrt(3)[/math]. Therefore, the angle measures of this triangle are either [math]30°-60°-90°[/math] or [math]45°-45°-90°[/math].
Right Triangle ABC v1
  1. True
  2. False
3. 
For triangle ABC below, if [math]sin(B) = sqrt(2)/2[/math], its angle measures are either [math]45°-45°-90°[/math] or [math]30°-60°-90°.[/math]
Right Triangle ABC v2
  1. True
  2. False
4. 
The side lengths of [math]Delta ABC[/math] are [math]AB = 1 \ "unit", \ AC = sqrt(3) \ "units", BC = 2 \ "units"[/math]. What is the value of [math]sin(C) ?[/math]
Right Triangle ABC v2
  1. [math]1/2[/math]
  2. [math]sqrt(3)/2[/math]
  3. [math]1/sqrt(3)[/math]
  4. [math]sqrt(3)[/math]
5. 
The side lengths of triangle ABC are: [math]AB = 1 \ "unit", \ AC = 1 \ "unit", \ BC = sqrt(2) \ "units"[/math]. What is the value of [math]tan(B) ?[/math]
Right Triangle ABC v1
  1. [math]sqrt(2)[/math]
  2. [math]1/sqrt(2)[/math]
  3. [math]0[/math]
  4. [math]1[/math]
6. 
The side lengths of triangle ABC are as follows: [math]AC = 4sqrt(3) \ "units", \ BC = 4 \ "units", \ AB = 8 \ "units"[/math]. What is the value of [math]cos(A) ?[/math]
Right Triangle ABC v3
  1. [math]4/sqrt(3)[/math]
  2. [math]1/2[/math]
  3. [math]sqrt(3)/2[/math]
  4. [math]sqrt(3)/8[/math]
7. 
The side lengths of triangle ABC are as follows: [math]AB = (2sqrt(3))/3 \ "units", \ BC = sqrt(3)/3 \ "units", \ AC = 1 \ "unit"[/math]. What is the value of [math]tan(B) ?[/math]
Right Triangle ABC v3
  1. [math]1/sqrt(3)[/math]
  2. [math]sqrt(3)[/math]
  3. [math](2sqrt(3))/3[/math]
  4. [math]sqrt(3)/2[/math]
8. 
For triangle ABC, [math]cos(C) = 1/sqrt(2)[/math]. What is the value of [math]BC[/math] if [math]AC = sqrt(3) \ "units"?[/math]
Right Triangle ABC v2
  1. [math]sqrt(2) \ "units"[/math]
  2. [math]sqrt(3)/2 \ "units"[/math]
  3. [math]sqrt(6) \ "units"[/math]
  4. [math]1 \ "unit"[/math]
9. 
In triangle ABC, [math]sin(C) = 1/2[/math]. If [math]AC = 6 \ "units"[/math], what is the length of [math]bar{BC} ?[/math]
Right Triangle ABC v2
  1. [math]2 \ "units"[/math]
  2. [math]2sqrt(3) \ "units"[/math]
  3. [math]12 \ "units"[/math]
  4. [math]4sqrt(3) \ "units"[/math]
10. 
In triangle ABC [math]tan(B) = sqrt(3)[/math]. What is the length of [math]bar{BC}[/math] if [math]AB = 1/4 \ "unit" ?[/math]
Right Triangle ABC v3
  1. [math]1/8 \ "unit"[/math]
  2. [math]sqrt(3)/12 \ "units"[/math]
  3. [math]4 sqrt(3) \ "units"[/math]
  4. [math]1 \ "unit"[/math]

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