CCSS.Math.Content.HSG-SRT.C

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

• CCSS.Math.Content.HSG-SRT.C.6

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

• CCSS.Math.Content.HSG-SRT.C.7

  Explain and use the relationship between the sine and cosine of complementary angles.

• CCSS.Math.Content.HSG-SRT.C.8

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

01

What Students Need to Do

Students define sine, cosine, and tangent as side-length ratios in right triangles. They use those ratios and inverse trigonometric functions to find missing side lengths and angle measures.

02

What Mastery Looks Like

Students correctly label the hypotenuse, opposite side, and adjacent side from a chosen angle. They select a suitable ratio, solve for a missing side or angle, and check that the answer fits the diagram.

03

Common Misconceptions

Students often label opposite and adjacent sides without using the marked reference angle. They may confuse sine, cosine, and tangent, or use inverse functions when finding a side. Some round too early or leave calculators in radian mode.

04

How to Assess It

Give a right triangle with a 38° angle and adjacent side 12 cm. Ask students to find the opposite side and hypotenuse, showing both ratio choices.

1. 01

   Build a paper clinometer with a protractor, straw, and string, then measure an angle and estimate the classroom ceiling height.

2. 02

   Ask students to explain why the sine of an angle stays constant for similar right triangles of different sizes.

3. 03

   Run a triangle card sort matching diagrams, missing sides, given angles, correct ratios, and calculator answers.

4. 04

   Use a wheelchair ramp plan to calculate the rise, run, angle, and ramp length, then check whether the measurements agree.

• CCSS.Math.Content.HSG-SRT.D

  Apply trigonometry to general triangles

• CCSS.Math.Content.HSF-TF.C

  Prove and apply trigonometric identities