CCSS.Math.Content.HSG-SRT.C.8
The Standard
Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.
Common Core State Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students draw or label a right triangle from a real situation and identify known and unknown measures. They choose sine, cosine, tangent, or the Pythagorean Theorem to find missing sides or angles.
What Mastery Looks Like
- Given a diagram or context, students choose an efficient equation and solve for unknown sides or angles. They include units, round as directed, and check that the answer fits the situation.
Common Misconceptions
- Students label opposite and adjacent sides without using the given angle. They may treat the longest visible side as the hypotenuse or choose the wrong ratio. Calculator degree mode, inverse functions, and early rounding also cause errors.
How to Assess It
- Exit ticket: A 10-meter ladder makes a 68-degree angle with the ground. Find the wall height and the ladder's distance from the wall, to the nearest tenth.
Lesson moves
Ways to Teach It
Students use a clinometer and tape measure to collect angle and distance data, then calculate the height of a wall or tree.
Ask students to explain why the opposite and adjacent sides change when the reference angle changes in the same triangle.
Play a card sort matching right triangle diagrams, known values, unknown values, and the correct sine, cosine, tangent, or Pythagorean equation.
Give students a roof pitch, building width, and rafter diagram, then have them calculate the roof rise and rafter length.
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Printable HSG-SRT.C.8 Worksheet
A ready-to-print activity worksheet aligned to CCSS.Math.Content.HSG-SRT.C.8, with an answer key for the teacher on its own page. No account needed.
PDF, US Letter, prints cleanly in black and white.
Download the worksheetLearning progression
Where This Standard Sits
Before This Standard
If students are struggling here, check these first.
- CCSS.Math.Content.HSG-SRT.C.6
Students must know sine, cosine, and tangent as angle-based side ratios before using them to find missing sides or angles.
- CCSS.Math.Content.8.G.B.7
Solving applied right triangles in high school still requires finding missing sides with the Pythagorean Theorem before adding trigonometric ratios.
- CCSS.Math.Content.HSA-CED.A.4
Solving right triangles often requires isolating a missing side or angle from trig ratios or the Pythagorean formula.
What This Unlocks
Mastery here sets students up for these next.
- CCSS.Math.Content.HSG-SRT.D.10
Right triangle sine, cosine, and the Pythagorean Theorem are used to derive and apply the Laws of Sines and Cosines.
- CCSS.Math.Content.HSG-SRT.D.11
Right-triangle trig and Pythagorean reasoning support interpreting sine, cosine, sides, and angles before using general triangle laws.
- CCSS.Math.Content.HSN-VM.B.4b
Finding vector components and the resultant’s length and angle requires right triangle trigonometry and the Pythagorean Theorem.
- CCSS.Math.Content.HSG-SRT.D.9
Deriving the area formula requires using sine in the right triangle formed by the altitude to express the height.
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