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The Sun's Angle, Exactly

Part of the Right-Triangle Trigonometry section of Coddy's Trigonometry journey. Lesson 50 of 50.

A flagpole 20 m tall casts a shadow 20√3 m long, about 34.64 m. What is the sun's angle of elevation, exactly?

Challenge

A pole 20 m tall casts a shadow 20√3 m long. Find the sun's angle of elevation θ exactly. Then press Check.

Try it yourself

$Use the figure to find theta$

Use the figure to find theta

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

All lessons in Right-Triangle Trigonometry

1Sides of a Right Triangle

How Tall Is the Tree?The Hypotenuse The Opposite Side The Adjacent Side When the Angle Moves Recap: Naming the Sides

4Finding the Hypotenuse

The Unknown Below the Bar How Long Is the Kite String?A Leg Below the Bar Is the Answer Sensible?Recap: The Hypotenuse

7Elevation and Depression

Angle of Elevation Measuring From Eye Level Angle of Depression The Sun's Angle Two Triangles, One Height Recap: Looking Up and Down

2The Three Ratios

The Sine Ratio The Cosine Ratio The Tangent Ratio Choosing the Ratio Recap: The Three Ratios

5Finding an Angle

Inverse Sine Inverse Cosine Inverse Tangent The Angle of a Ramp Both Acute Angles Recap: Finding an Angle

8Reciprocal Ratios

Cosecant, Secant, Cotangent Exact Reciprocal Values A Side From a Cosecant A Ladder and a Secant Recap: Reciprocal Ratios

3Finding a Side

Sides at Any Angle Rounding the Answer Tangent: Leg From Leg A Ladder Against a Wall The Other Acute Angle Recap: Finding a Side

6Special Triangles, Exactly

The Two Special Triangles An Exact Hypotenuse The Side Next to 30°An Exact Angle Recap: Exact Values

9Final Challenges

Is the Ladder Safe?The Wheelchair Ramp Two Observers The Landing Plane The KiteThe Sun's Angle, Exactly