Home›Lesson Plans›Mathematics›Geometry · Grade 10

Right Triangle Trig: SOH-CAH-TOA

Students unlock trigonometry — the sine, cosine, and tangent ratios — discovering how the angles of a right triangle are tied to the ratios of its sides, and using SOH-CAH-TOA to find missing sides and angles.

Grade 10Trigonometry50 minutes1 class periodGradual ReleaseExplicit teaching4 StandardsCommon Core
Start the Lesson
Lesson at a Glance

Everything you need before the bell rings

Learning Objectives

Students will be able to…

  • ✓Define sine, cosine, tangent.
  • ✓Use SOH-CAH-TOA.
  • ✓Find a missing side.
  • ✓Find a missing angle.
Essential Question

Give me one angle and one side of a right triangle, and I can find every other part. What is the hidden connection between angles and side ratios?

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Lesson Phases
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Vocabulary Terms
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Standards Aligned
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Interactive Task
Model · Interactive Tool

The Trig Explorer

Project this and change the angle. Watch the triangle reshape and the sine, cosine, and tangent ratios update — SOH-CAH-TOA in action.

📐 Change the angle — watch sin, cos, tanTry it
Angle θ: 37°

The Lesson · Gradual Release (I Do · We Do · You Do)

50 minutes, five moves

Tap any phase to open the teacher moves and student actions.

1

Launch — One Angle, Every Side

5 min

How can one angle unlock every side of a right triangle?

👩‍🏫 Teacher Moves

  • Pose the ramp/ladder problem.
  • Ask what links angle and sides.
  • Set the goal: trig ratios.

🎒 Student Actions

  • Consider the problem.
  • Wonder about the link.
  • Predict the idea.
2

I Do — SOH-CAH-TOA

10 min

Teacher models.

👩‍🏫 Teacher Moves

  • Define opposite, adjacent, hypotenuse.
  • Define sin, cos, tan as ratios.
  • Teach SOH-CAH-TOA.

🎒 Student Actions

  • Label the sides.
  • Learn the ratios.
  • Learn the mnemonic.
3

We Do — Explore Together

13 min

Class uses the Trig Explorer.

👩‍🏫 Teacher Moves

  • Change the angle; read ratios.
  • Connect ratio to side lengths.
  • Set up a ratio for a problem.

🎒 Student Actions

  • Change the angle.
  • Read the ratios.
  • Set one up.
4

You Do — On Your Own

12 min

Students solve triangles.

👩‍🏫 Teacher Moves

  • Find missing sides with trig.
  • Find a missing angle (inverse).
  • Solve a real problem.

🎒 Student Actions

  • Find sides.
  • Find angles.
  • Solve a problem.
5

Close — Close

5 min

One triangle.

👩‍🏫 Teacher Moves

  • Give an angle and a side.
  • Find a missing side.
  • Hand out the exit ticket.

🎒 Student Actions

  • Find the side.
  • Show the ratio.
  • Complete the exit ticket.
Standards Alignment

Built to the standards you report on

Aligned to the Common Core State Standards for Mathematics (High School: Geometry).

CCSS
G-SRT.6

Define trigonometric ratios for acute angles in right triangles.

CCSS
G-SRT.7

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

CCSS
G-SRT.8

Use trigonometric ratios and the Pythagorean theorem to solve right triangles.

CCSS
G-SRT.5

Use similarity criteria (which underlie trig ratios) to solve problems.

Differentiation

One lesson, every learner

Multilingual Learners

ELL / EMERGING READERS
  • Label opp/adj/hyp on a diagram.
  • Sentence frame: “sinθ = opposite over hypotenuse.”
  • Use the SOH-CAH-TOA card.

Support & Access

IEP / 504
  • Start with tangent only.
  • Provide the formulas.
  • Use a calculator for ratios.

Stretch & Extend

GIFTED / EARLY FINISHERS
  • Use inverse trig to find angles.
  • Solve angle-of-elevation problems.
  • Derive the sine-cosine complement rule.
Materials

What to gather

  • 📽️Projector / board
  • 📓Math notebooks
  • 💻The Trig Explorer
  • 🧮Scientific calculators
  • 📐Protractors
  • 🎫Exit-ticket slips
Vocabulary

Key terms — hover for a quick definition

trigonometrythe study of triangle side-angle relationshipssineopposite ÷ hypotenusecosineadjacent ÷ hypotenusetangentopposite ÷ adjacentoppositethe side across from the angleadjacentthe side next to the anglehypotenusethe longest side (opposite the right angle)inverse trigfinds an angle from a ratio
Evaluate

Exit Ticket

Preview the three formative checks. Tap “Sample answer” to see what mastery looks like — hide them before you print for students.

QUESTION 1
What does SOH-CAH-TOA stand for?
Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent.
QUESTION 2
In a right triangle, the side opposite a 30° angle is 5 and the hypotenuse is 10. What is sin(30°)?
0.5 (5 ÷ 10).
QUESTION 3
Which ratio would you use to find a side if you know the angle, the adjacent side, and want the opposite side?
Tangent (tanθ = opposite/adjacent).

Going deeper? Angles of elevation.

Have students solve angle-of-elevation and depression problems — like finding a building’s height from a distance and an angle. A printable trig sheet is in the Math library.

Study · Flashcards

Study the key terms

Tap a card to flip it, then rate whether you knew it. Built from this lesson’s vocabulary.

🃏 Right Triangle TrigonometryFlip
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Practice · Quiz

Check your understanding

A quick self-check with instant feedback, drawn from this lesson’s key terms.

📝 Right Triangle TrigonometryQuiz
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Question 1
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Practice · Worksheet

Printable worksheet

A print-and-go review sheet with a built-in answer key. Tap “Show answer key” to reveal answers, or print the clean version for students.

🖨️ Right Triangle TrigonometryPrint
Name: ________________________
Date: ____________

Part A · Write the word that matches each meaning

Word bank: adjacent, cosine, hypotenuse, inverse trig, opposite, sine, tangent, trigonometry
  1. finds an angle from a ratio
  2. the side across from the angle
  3. opposite ÷ hypotenuse
  4. opposite ÷ adjacent
  5. the side next to the angle
  6. adjacent ÷ hypotenuse
  7. the study of triangle side-angle relationships
  8. the longest side (opposite the right angle)

Part B · Show what you learned

  1. What does SOH-CAH-TOA stand for?
  2. In a right triangle, the side opposite a 30° angle is 5 and the hypotenuse is 10. What is sin(30°)?
  3. Which ratio would you use to find a side if you know the angle, the adjacent side, and want the opposite side?
Answer key — Part A: 1) inverse trig · 2) opposite · 3) sine · 4) tangent · 5) adjacent · 6) cosine · 7) trigonometry · 8) hypotenuse
Part B: 1) Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent. 2) 0.5 (5 ÷ 10). 3) Tangent (tanθ = opposite/adjacent).