Navigator Teacher Guide Navigator Teacher Guide
Solving Non-Right Triangles • Tier 2 Intervention
Standard
CO HS.G-SRT.D.11
Lesson Objective
Students will be able to analyze given information in non-right triangles (SAS, SSS, ASA, AAS, SSA) to determine whether to use the Law of Sines or the Law of Cosines and execute the calculation to find missing side lengths or angle measures.
Target Population
Tier 2 intervention for students who struggle with identifying patterns in geometric figures or those who have difficulty managing multi-step algebraic procedures.
Key Concepts
Law of Sines: Best for "Pairs" (Angle and Opposite Side).Law of Cosines: Best for "Sandwich" (SAS) or "All Sides" (SSS).Non-Right Triangles: Triangles without a 90° angle.
Instructional Delivery
01 Identify
The "Pair" Hunt (10 mins)
Use the Navigator Slides to model finding "known pairs" (an angle and its opposite side). If a pair exists, use Sines. If not, use Cosines. Use the phrase "The Sines need a Sign (Pair)."
02 Map
Blueprint Analysis (10 mins)
Hand out the Strategy Blueprint Guide . Have students color-code triangles: Blue for Sines (Pairs) and Orange for Cosines (No Pairs). Don't solve yet—just categorize.
03 Apply
Scaffolded Missions (20 mins)
Students work through the Mission Briefing Worksheet . Start with Level 1 (Identifying the law) before moving to Level 2 (Setting up) and Level 3 (Solving).
Common Misconceptions
Wrong Law Choice: Students often try to use Law of Sines for SAS because the formula is simpler. Remind them: "No pair, no Sines."Calculator Mode: Ensure students are in DEGREE mode, not Radian mode.The SSS Angle: Remind students to find the largest angle first with Law of Cosines to avoid ambiguous cases later.
Progress Monitoring
Use the Precision Check Exit Ticket at the end of the session.
SCORE ACTION
0-1 correct Review "Pair" identification.
2 correct Check for algebraic setup errors.
3 correct Ready for Ambiguous Case extension.
Navigator Slides Geometry Intervention
Triangle
Navigator
Mastering the Law of Sines and Law of Cosines for any triangle.
The Big Question
We know how to solve Right Triangles using SOH CAH TOA...
But what if there is no 90° angle?
When the right angle disappears, we need stronger tools.
? ? ?
Your Navigation Tools
Law of Sines
\[ \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} \]
"Best for finding parts when you have a matching pair."
Law of Cosines
\[ a^2 = b^2 + c^2 - 2bc \cos A \]
"Best for when you don't have any matching pairs."
The "Pair" Hunt
A Pair is a Side and its Opposite Angle .
I HAVE A PAIR
Use Law of Sines .
NO PAIRS FOUND
Use Law of Cosines .
Strategy Map
Start: Analyze Triangle
Do you have an Angle and its Opposite Side?
YES
NO
Law of SINES
(AAS, ASA, SSA)
Law of COSINES
(SAS, SSS)
Mission 1
Case AAS
42° 105° x = ? 12 cm
The Checklist:
Look for a known pair...
Pair found! (105° and 12 cm)
Strategy: Law of Sines
Mission 2
Case SAS
55° 15 m 8 m x = ?
The Checklist:
Look for a known pair...
No pairs! (SAS Sandwich)
Strategy: Law of Cosines
Ready to Pilot?
1
Grab Your Blueprint
2
Analyze Your Mission
3
Solve the Unknowns
Strategy Blueprint Guide Technical Reference 01-A
Triangle Strategy
Blueprint
Subject
Oblique Triangles
Tools
Sines & Cosines
Decision Flowchart: The "Pair" Hunt
Analyze Given Info
Do you have a matching PAIR?
(A side and its opposite angle are both known)
YES
LAW OF SINES
Use for: ASA, AAS, SSA
\[ \frac{a}{\sin A} = \frac{b}{\sin B} \]
NO
LAW OF COSINES
Use for: SAS, SSS
\[ a^2 = b^2 + c^2 - 2bc \cos A \]
Sines: The "Pairs"
AAS (Pair Exists)
SSA (Pair Exists)
Cosines: No Pairs
SAS (The Sandwich)
SSS (All Sides)
Always check Degree Mode.
Use Cosines for the largest angle in SSS.
Triangle Navigator v1.0
Mission Briefing Worksheet Mission Briefing
Triangle Navigation & Problem Solving
Pilot Name
Date
Level 1
Radar Identification
Determine which Law is required based on the "Pair Hunt".
40° 110° 15
Law of Sines
Law of Cosines
12 10 8
Law of Sines
Law of Cosines
65° 22 18
Law of Sines
Law of Cosines
35° x 14 48°
Law of Sines
Law of Cosines
Level 2
Flight Path Setup
Identify the law AND write the equation setup. (Do not solve yet)
42° x 15 cm 115°
Chosen Law
Equation Setup
58° 7 m 9 m x
Chosen Law
Equation Setup
Level 3
Landing Target
Full Mission: Choose, Setup, and Solve to the nearest tenth.
50° 75° 14.2 x
Show Your Work
Calculated Result
x = ______
11 8 16 θ
Find the measure of angle θ.
Show Your Work
Calculated Result
θ = ______°
Flight Code: GEO-T2-SINCOS Triangle Navigator System • Tier 2 Support
