Trig Blueprint Worksheet
Trig Blueprint
Structural Review: Sides & Angles
Name:
Date:
SOH
Sin(θ) = Opp / Hyp
CAH
Cos(θ) = Adj / Hyp
TOA
Tan(θ) = Opp / Adj
Blueprint for Success
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1
Label: Based on the angle (θ), identify Opposite (O), Adjacent (A), and Hypotenuse (H).
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2
Select: Look at what you HAVE and what you NEED. Pick Sin, Cos, or Tan.
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3
Setup: Plug your values into the ratio formula.
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4
Solve: Rearrange and calculate. Use inverse (\(\sin^{-1}\), \(\cos^{-1}\), \(\tan^{-1}\)) for angles!
Example 1: Finding a Side
12 x 32°
Label: O = 12, A = x
Ratio: O & A → Tan
Setup: \( \tan(32^\circ) = \frac{12}{x} \)
Solve: \( x = \frac{12}{\tan(32^\circ)} \approx 19.2 \)
Example 2: Finding an Angle
15 9 θ
Label: A = 9, H = 15
Ratio: A & H → Cos
Setup: \( \cos(\theta) = \frac{9}{15} \)
Solve: \( \theta = \cos^{-1}(0.6) \approx 53.1^\circ \)
Architect's Field Note
When finding a side, if your variable is in the denominator, you divide the side by the ratio value. If your variable is in the numerator, you multiply the side by the ratio value.
Drafting Table Practice
Find the missing value for each triangle. Round all answers to the nearest tenth.
1
Find side x
24 cm x 40°
2
Find angle θ
7 11 θ
3
Find side y
18 in y 28°
4
Find side z
35 ft z 48°
Trig Blueprint Answer Key
Trig Blueprint
Answer Key & Solution Paths
Teacher Resource
1
Missing Side (Tangent)
Identified Sides: Opp: x, Adj: 24
Equation: \( \tan(40^\circ) = \frac{x}{24} \)
Calculation: \( x = 24 \cdot \tan(40^\circ) \)
Final Answer: 20.1 cm
2
Missing Angle (Tangent)
Identified Sides: Opp: 11, Adj: 7
Equation: \( \tan(\theta) = \frac{11}{7} \)
Calculation: \( \theta = \tan^{-1}(\frac{11}{7}) \)
Final Answer: 57.5°
3
Missing Side (Sine)
Identified Sides: Opp: y, Hyp: 18
Equation: \( \sin(28^\circ) = \frac{y}{18} \)
Calculation: \( y = 18 \cdot \sin(28^\circ) \)
Final Answer: 8.5 in
4
Missing Side (Cosine)
Identified Sides: Adj: z, Hyp: 35
Equation: \( \cos(48^\circ) = \frac{z}{35} \)
Calculation: \( z = 35 \cdot \cos(48^\circ) \)
Final Answer: 23.4 ft
Teaching Tips:
- Mode Check: Always verify calculators are in Degree mode.
- Ratio Logic:
- #1: Uses Tan (O/A) to find height.
- #2: Uses Tan (O/A) to find base angle.
- #3: Uses Sin (O/H) to find height.
- #4: Uses Cos (A/H) to find base.
- Rounding: Remind students to only round at the very last step for maximum precision.
