CCSS.Math.Content.HSG-SRT.D

CCSS.Math.Content.HSG-SRT.D is a cluster heading. These are the individual standards under it.

• CCSS.Math.Content.HSG-SRT.D.10

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

• CCSS.Math.Content.HSG-SRT.D.11

  (+) 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, result...

• CCSS.Math.Content.HSG-SRT.D.9

  (+) Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.

01

What Students Need to Do

Students use side lengths and angle measures to solve triangles that are not necessarily right triangles. They choose among the Law of Sines, Law of Cosines, and trigonometric area formula, and justify why each applies.

02

What Mastery Looks Like

Students select an appropriate formula from the given sides and angles, then solve accurately for missing measures. They recognize when an SSA case has zero, one, or two solutions and check whether answers are reasonable.

03

Common Misconceptions

Students pair an angle with the wrong opposite side or use the wrong law for the given information. They may miss the two possible triangles in an SSA case, round too early, or leave calculators in radian mode.

04

How to Assess It

Give a triangle with sides 8 and 11 and an included angle of 47°. Ask students to find the third side and area, showing formulas and work.

1. 01

   Have students construct SSA triangles with rulers, protractors, and string, then record when zero, one, or two triangles are possible.

2. 02

   Ask students to explain when the Law of Sines is more useful than the Law of Cosines, using two labeled examples.

3. 03

   Run a card sort where students match triangle diagrams to Law of Sines, Law of Cosines, or area formula setups.

4. 04

   Give a surveying problem where students use two measured distances and an angle to calculate the distance across a pond.

• CCSS.Math.Content.HSG-SRT.C

  Define trigonometric ratios and solve problems involving right triangles

• CCSS.Math.Content.HSG-SRT.B.4

  Prove theorems about triangles.

• CCSS.Math.Content.HSF-TF.C

  Prove and apply trigonometric identities

• CCSS.Math.Content.HSG-SRT.C.8

  Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.