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Common Core Standard HSG-SRT.D.10 Questions

(+) Prove the Laws of Sines and Cosines and use them to solve problems.

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Grade 11 Trigonometry CCSS: HSG-SRT.D.10

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What is the missing reason in step 3?
  1. Definition of perpendicular lines
  2. Perpendicular Bisector Theorem
  3. All right angles are congruent
  4. Congruent supplementary angles are right angles
Grade 11 Trigonometry CCSS: HSG-SRT.D.10

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What is the missing reason in step 18?
  1. Given
  2. Exterior Angle Theorem
  3. Sum of the angles in a triangle is 180°
  4. Sum of the angles on a straight line is 180°
Grade 11 Trigonometry CCSS: HSG-SRT.D.10

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What is the missing reason in step 23?
  1. Previous result
  2. Transitive Property of Equality
  3. Multiplication Property of Equality
  4. Law of sines
Grade 11 Trigonometry CCSS: HSG-SRT.D.10

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What is the missing statement in step 5?
  1. sin(θ)=BCAC
  2. sin(θ)=BDDC
  3. sin(θ)=BDBC
  4. sin(θ)=DCBD
Grade 11 Trigonometry CCSS: HSG-SRT.D.10

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Is this proof also valid for the law of cosines formulas that include the other two angles of the triangle, namely AB2=BC2+AC2-2BC ACcos(mBCA) and AC2=AB2+BC2-2AB BCcos(mABC)?
  1. Yes. If altitudes were constructed from vertices A or C, the proofs for these two formulas would be identical to the one given.
  2. Yes. Since the formula including the angle with the largest measure has been proven, it must necessarily hold for the formulas including the other angles in the triangle.
  3. No. The most straightforward proof for these two formulas would be similar to the proof given for an acute triangle (and they would include constructing an altitude from vertex A only).
  4. No. The proof for either of these formulas would require additional trigonometric identities because of the obtuse angle.
Grade 11 Trigonometry CCSS: HSG-SRT.D.10

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What is the missing reason in step 12?
  1. Each of the three altitudes of an acute triangle intersects the side opposite the vertex through which the altitude passes
  2. The orthocenter of all acute triangles lies within the triangle
  3. Perpendicular Bisector Theorem (for triangles)
  4. All triangles have three altitudes
Grade 11 Trigonometry CCSS: HSG-SRT.D.10

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What is the missing statement in step 7?
  1. cos(θ)=ACBC
  2. cos(θ)=CDBC
  3. cos(θ)=BDBC
  4. cos(θ)=BDCD
Grade 11 Trigonometry CCSS: HSG-SRT.D.10

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The proof given applies to which type of triangles?
  1. All triangles.
  2. Acute triangles.
  3. Non-right triangles.
  4. Scalene triangles.
Grade 11 Trigonometry CCSS: HSG-SRT.D.10
In ΔABC, AB=10 units, BC=4 units, and mA=100°. Using the law of sines and the given information, which of the following is true?
  1. No such triangle exists.
  2. These measurements result in a unique triangle.
  3. These measurements result in two possible triangles.
  4. The law of sines cannot be used in this situation.
Grade 11 Trigonometry CCSS: HSG-SRT.D.10

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What is the missing statement in step 9?
  1. AC=AD+BD
  2. BD=AD+CD
  3. AC=AB+BC
  4. AC=AD+CD
Grade 11 Trigonometry CCSS: HSG-SRT.D.10
Which of the following is true concerning the law of cosines formula for a right triangle? Choose all correct answers.
  1. It simplifies to the Pythagorean Theorem for the right angle.
  2. It simplifies to the Pythagorean Theorem for all angles.
  3. It can be easily proven for the acute angles, mainly using the Pythagorean Theorem and the cosine ratio for that angle.
  4. It cannot be applied to right triangles.
Grade 11 Trigonometry CCSS: HSG-SRT.D.10

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What is the missing reason in step 1?
  1. Given
  2. Altitudes in non-right triangles do not intersect the other vertices of the triangle
  3. An altitude from the vertex of an obtuse angle in a triangle always intersects the opposite side
  4. The altitude of a triangle consists of infinitely many points
Grade 11 Trigonometry CCSS: HSG-SRT.D.10
In ΔFGH, FG=3 units, GH=2 units, and mF=30°. Using the law of sines and the given information, which of the following is true?
  1. No such triangle exists.
  2. These measurements result in a unique triangle.
  3. These measurements result in a two possible triangles.
  4. The law of sines cannot be used in this situation.
Grade 11 Trigonometry CCSS: HSG-SRT.D.10

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What is the missing reason in step 13?
  1. Distributive Property
  2. Substitution Property of Equality
  3. Pythagorean Identity
  4. Pythagorean Theorem
Grade 11 Trigonometry CCSS: HSG-SRT.D.10

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Grade 11 Trigonometry CCSS: HSG-SRT.D.10

This question is a part of a group with common instructions. View group »

What is the missing statement in step 5?
  1. sin(mB)=ADAB
  2. sin(mB)=ABAD
  3. sin(mB)=BDAB
  4. sin(mB)=BDAD
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