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Common Core Standard HSG-SRT.C.6 Questions

Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.

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Grade 11 Trigonometry CCSS: HSG-SRT.C.6
[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]
Grade 11 Trigonometry CCSS: HSG-SRT.C.6
Given that AC = 19 and AB = 11, find the measure of Angle B. Round to the nearest whole degree.
Right Triangle ABC v2
  1. [math]60deg[/math]
  2. [math]30deg[/math]
  3. [math]70deg[/math]
  4. [math]85deg[/math]
Grade 11 Trigonometry CCSS: HSG-SRT.C.6
[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]
Grade 11 Trigonometry CCSS: HSG-SRT.C.6
[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]
Grade 11 Trigonometry CCSS: HSG-SRT.C.6
[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.
Grade 11 Trigonometry CCSS: HSG-SRT.C.6
If AC = 16, BC = 18, what is the measure of angle A?
Right Triangle ABC v3
  1. 48.4°
  2. 41.6°
  3. 27.3°
  4. 62.7°
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