🌟 Trig Quest: Angles & Sides!

🔺 Right Triangle Basics

In a right triangle, the three sides are named based on their position relative to a reference angle θ:

SOH-CAH-TOA 🎵

SIN sin θ = opp ÷ hyp

COS cos θ = adj ÷ hyp

TAN tan θ = opp ÷ adj

INVERSE To find angle: sin⁻¹, cos⁻¹, tan⁻¹

📖 Example Problem 1 — Find the Angle

🏗️ Ladder Problem

A 16 ft ladder is placed 14 ft away from a tree. At what angle of elevation must the ladder be to reach the top?

1

Identify: Hypotenuse = 16 ft (ladder), Adjacent = 14 ft (distance from tree), we need angle θ.

2

Choose ratio: We know adj and hyp → use cos θ = adj/hyp

3

Set up: cos θ = 14/16 = 0.875

4

Solve: θ = cos⁻¹(0.875) ≈ 28.96° ✅

📖 Example Problem 2 — Find a Side

🎣 Fishing Line Problem

A 20 ft tree is at a 15° angle of elevation from the student. How long is the fishing line?

1

Identify: Opposite = 20 ft (tree height), angle θ = 15°, find Hypotenuse (line).

2

Choose ratio: We know opp and angle → use sin θ = opp/hyp

3

Rearrange: hyp = opp / sin θ = 20 / sin(15°)

4

Solve: hyp = 20 / 0.2588 ≈ 77.3 ft ✅

🎯 Choose Your Problem!

Pick any problem you want to solve. You need to answer 3 multiple-choice questions per problem. Get all 3 right for full credit! 🌟

✅ = Solved correctly ❌ = Needs retry ⬜ = Not attempted

Problem 1

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2

3

Get all 3 right! ✨

🏆 Your Results!

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Trig Quest!