CCSS.Math.Content.HSG-SRT.D.11
The Standard
(+) Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces).
Common Core State Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students use known side lengths and angle measures to find missing parts of a triangle. They decide which rule fits the given information and use it in diagrams and applied problems.
What Mastery Looks Like
- Students choose a suitable rule from the given sides and angles, then solve accurately. They check that side lengths are reasonable, angles total 180°, and answers include correct units.
Common Misconceptions
- Students match sides with the wrong opposite angles or use the sine rule without a known opposite pair. They may miss the two possible triangles in an SSA case, use the wrong calculator mode, or round too early.
How to Assess It
- Exit ticket: In triangle ABC, a = 8, b = 11, and C = 52°. Find c, A, and B to the nearest tenth, and name each rule used.
Lesson moves
Ways to Teach It
Place three taped points on the floor, measure two sides and the included angle, then calculate and verify the third side.
Give three triangle diagrams and ask, “Which rule would you use first, and what given information makes that choice work?”
Run a card sort with SSS, SAS, SSA, ASA, and AAS cases, then have pairs solve one card from each group.
Give students two survey points and sighting angles to a tree, then have them calculate the tree’s distance from each point.
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Printable HSG-SRT.D.11 Worksheet
A ready-to-print activity worksheet aligned to CCSS.Math.Content.HSG-SRT.D.11, with an answer key for the teacher on its own page. No account needed.
PDF, US Letter, prints cleanly in black and white.
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Where This Standard Sits
Before This Standard
If students are struggling here, check these first.
- CCSS.Math.Content.HSG-SRT.C.8
Right-triangle trig and Pythagorean reasoning support interpreting sine, cosine, sides, and angles before using general triangle laws.
- CCSS.Math.Content.HSG-SRT.D.10
Deriving and using the Laws of Sines and Cosines supports applying them to solve varied triangle measurement problems.
- CCSS.Math.Content.HSA-CED.A.4
Isolating sides or angles in sine and cosine formulas uses the same equation-rearranging skills from formula work.
Keep exploring
Related Standards
- CCSS.Math.Content.HSF-TF.B.7
(+) Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms...
- CCSS.Math.Content.HSF-TF.C.9
(+) Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.
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