Angle Architects Lesson Plan Angle Architects
Lesson Plan: Right Triangle Trigonometry
Duration: 50 Minutes
Topic: Sine, Cosine, Tangent
Learning Objective
Students will define and apply the trigonometric ratios (sine, cosine, tangent) to solve for missing side lengths and angles in right triangles within architectural and construction contexts.
CCSS Standards
HSG.SRT.C.6
Required Materials
Blueprint Bell Ringer (Pre-test)
Structure & Sine Slides
Drafting Data Guided Notes
Construction Calculations Practice
Site Survey 10-Question Quiz
Scientific Calculators (Degree Mode)
50-Minute Pacing Guide
00-05m
Bell Ringer & Pre-Test
Material: Blueprint Bell Ringer
Quick assessment of Pythagorean Theorem and side identification.
05-20m
Direct Instruction
Materials: Slides + Guided Notes
Introduction to SOH CAH TOA. Demonstration of architecture applications.
20-25m
Flashcard Drill
Material: Trig Toolkit Flashcards
Rapid-fire partner review of ratio definitions and side names.
25-40m
Construction Workshop
Material: Practice Sheet
Application to real-world problems: roof pitches and ADA ramps.
40-50m
Site Survey Quiz
Material: Practice Quiz
Formal individual assessment (10 questions).
Instructional Strategies
Common Pitfalls
Degree Mode: Students often forget to set calculators correctly.Side Switching: Confusing "Opposite" and "Adjacent" when the angle of focus changes.
Key Questioning
"If you're standing at the bottom of an ADA ramp looking up, is the height of the door 'opposite' or 'adjacent' to you?"
Blueprint Bell Ringer Pre-Test Blueprint Bell Ringer
Phase 01: Initial Site Assessment
ARCHITECT: ____________________
DATE: ________
01
The Structural Brace
Calculate the exact length of the diagonal brace using the Pythagorean Theorem: \(a^2 + b^2 = c^2\).
6 ft 8 ft Brace (c)
Calculations
Length:
02
The Angle Perspective
Label the sides relative to the indicated angle \( \theta \).
\( \theta \) SIDE A: SIDE B: SIDE C:
Side A
Side B
Side C
Geometry: Right Triangle Unit Ref: BP-101.B
Structure and Sine Slides Structural Engineering 101
STRUCTURE & SINE
Trigonometry for Construction and Architecture
The Trig Toolkit: SOH CAH TOA
SINE
O / H
Opposite / Hypotenuse
COSINE
A / H
Adjacent / Hypotenuse
TANGENT
O / A
Opposite / Adjacent
Case Study #01
Roof Rafters
A house is 24ft wide. The roof rises at 30°. How long is the rafter?
"We have Adjacent (12ft) and Angle (30°). We need Hypotenuse."
12 ft H = ? 30°
Calculation
Step 1: Choose Ratio
\(\cos(30^\circ) = \frac{12}{H}\)
Step 2: Solve for H
\(H = \frac{12}{\cos(30^\circ)}\)
\(H \approx 13.86\text{ ft}\)
Guided Practice
ADA Ramp
A door is 30 inches high. The ramp angle must be 4.8°. How long is the ramp base (A)?
Which ratio should we use to find the Adjacent side if we have the Opposite side?
30" A = ? 4.8°
Drafting Data Guided Notes Drafting Data
Trigonometry Field Notes
Site: _________________
Architect: ______________
1. Essential Ratios: SOH CAH TOA
SINE
\( \frac{Opp}{Hyp} \)
COSINE
\( \frac{Adj}{Hyp} \)
TANGENT
\( \frac{Opp}{Adj} \)
\( \theta \)
Define the sides for \( \theta \):
Opposite:
Adjacent:
Hypotenuse:
2. Solve Protocol
1 Identify the known angle and given sides relative to it.
2 Select the correct ratio (SOH, CAH, or TOA) to use.
3 Set up the equation and substitute the values.
4 Solve for the missing variable using algebraic steps.
3. Sample: The ADA Ramp
A door is 30 inches high. The ramp angle is 4.8°. Find the ramp length (Hypotenuse).
Workspace / Sketch Here
RESULT: ____________
CCSS.MATH.HSG.SRT.C.8 Structure Survey v1.3
Trig Toolkit Flashcards Trig Toolkit Flashcards
SOH CAH TOA Architect Edition
Cut along outer border
SINE
Front
\( \frac{Opp}{Hyp} \)
Opposite / Hypotenuse
COSINE
Front
\( \frac{Adj}{Hyp} \)
Adjacent / Hypotenuse
TANGENT
Front
\( \frac{Opp}{Adj} \)
Opposite / Adjacent
HYPO
Front
Definition
The side opposite the right angle. Always the longest side.
Assembly: Cut out each 320x400 rectangle. Fold down the middle dashed line to create double-sided reference cards. Secure with tape or glue.
Construction Calculations Practice Field Practice Worksheet
Construction Calculations
REF: 44.802.TRG
PHASE: APPLICATION
Surveyor: ________________________ Date: ________
1
The Gable Roof Design
A roof rises 7 inches for every 12 inches of horizontal run. Find the angle of elevation \( \theta \) using the inverse tangent function.
7 in 12 in \( \theta \)
Calculations Area
ANGLE \( \theta \):
2
ADA Compliance
A door is 30 inches above the ground. If the maximum ramp angle is 4.8°, what is the minimum required ramp length (hypotenuse)?
Sketch your triangle and solve here
Selected Ratio: _______________ Final Length: _______________
3
Crane Stability
A 150ft cable forms a 25° angle with a vertical skyscraper. Calculate the ground distance between the building base and the anchor point.
Show step-by-step setup
Ground Dist: ____________
Site Survey Practice Quiz Site Survey Quiz
Trigonometry Mastery Assessment
SCORE: ____ / 10
Name: ________________________________________ Date: ____________
I. Fundamentals (4 Points)
1. In SOH CAH TOA, "O" stands for:
2. The ratio for COSINE is:
3. TANGENT is calculated as:
4. The longest side of a right triangle is:
II. Survey Analysis (6 Points)
Round answers to 2 decimal places. Show work for credit.
A 12ft ladder leans against a wall at 75° to the ground. How high does it reach?
Work Area
RESULT: ______________
A tower stands 50m away. The angle to the top is 35°. Find the height.
Work Area
RESULT: ______________
7. Find \( x \): \( \sin(30^\circ) = \frac{x}{20} \)
8. Find \( \theta \): \( \tan(\theta) = 1.0 \)
9. Find \( y \): \( \cos(60^\circ) = \frac{5}{y} \)
10. Find \( \sin(45^\circ) \):
REF: BP-101-TRIG Property of Blueprint Academy © 2026
Angle Architects Answer Key Official Answer Key
Teacher Reference: Angle Architects
I. Bell Ringer
1. Structural Brace
\( 6^2 + 8^2 = c^2 \implies 36 + 64 = 100 \)
Answer: 10 ft
2. Perspective Labels
Side A: Opposite
Side B: Adjacent
Side C: Hypotenuse
II. Construction Practice
1. Roof Pitch Angle
\( \tan(\theta) = 7/12 \implies \theta = \tan^{-1}(0.58) \)
Answer: 30.26°
2. ADA Compliance
\( \sin(4.8) = 30/H \implies H = 30/\sin(4.8) \)
Answer: 358.42 in
3. Crane Stability
\( \sin(25) = x/150 \implies x = 150 \cdot \sin(25) \)
Answer: 63.39 ft
III. Site Survey Quiz
Opposite
35.01 m
Adj / Hyp
x = 10
Opp / Adj
θ = 45°
Hypotenuse
y = 10
11.59 ft
0.71
© 2026 Blueprint Academy Degree Mode Required for all Calculations
