Florida B.E.S.T. MA.912.T.1.3
The Standard
Apply the Law of Sines and the Law of Cosines to solve mathematical and real-world problems involving triangles.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students identify the known sides and angles in a triangle and label opposite pairs. They choose the Law of Sines or Law of Cosines, calculate missing measures, and interpret the result in context.
What Mastery Looks Like
- Given enough side and angle measures, students select the appropriate law and find missing measurements accurately. They label opposite pairs, use inverse functions correctly, and check whether each answer makes sense for the triangle.
Common Misconceptions
- Students often match a side with the wrong opposite angle. They may use the Law of Cosines when no included angle is known, or misuse inverse sine when finding an angle. Some assume every set of measurements makes exactly one triangle.
How to Assess It
- Exit ticket: A triangular garden has sides of 7 meters and 10 meters with an included angle of 42°. Find the third side to the nearest tenth and name the law you used.
Lesson moves
Ways to Teach It
Lay tape to make a triangle, measure two sides and the included angle, calculate the third with the Law of Cosines, then verify.
Ask: Which law fits each data set, and what known measurements make that choice valid? Students defend choices in two sentences.
Give pairs a card sort of SSS, SAS, ASA, AAS, and SSA triangles; they choose a law and solve one card.
From two points 20 meters apart, measure angles to a flagpole and use the Law of Sines to find its distance.
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Printable MA.912.T.1.3 Worksheet
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Related Standards
- MA.8.GR.2.4
Solve mathematical and real-world problems involving proportional relationships between similar triangles.
- MA.912.T.1.2
Solve mathematical and real-world problems involving right triangles using trigonometric ratios and the Pythagorean Theorem.
- MA.8.GR.1.1
Apply the Pythagorean Theorem to solve mathematical and real-world problems involving unknown side lengths in right triangles.
- MA.912.T.1.8
Solve mathematical and real-world problems involving one-variable trigonometric ratios.
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