The Sun's Angle
Part of the Right-Triangle Trigonometry section of Coddy's Trigonometry journey. Lesson 37 of 50.
Elevation works backwards too: from two lengths you can find the angle. The sun's angle of elevation is the angle its rays make with the ground, and any upright object and its shadow give it.
A person 1.8 m tall casts a shadow 3.1 m long. The height is opposite the sun's angle and the shadow is adjacent, so tan(theta) = 1.8/3.1 and theta = atan(1.8/3.1), about 30.14°. A short shadow means a high sun: at noon in midsummer shadows are short, and in winter the sun stays low and every shadow is long.
Challenge
A pole 3 m tall casts a shadow 4.2 m long on level ground. Find the sun's angle of elevation θ in degrees, to two decimal places. Then press Check.
Try it yourself
Use the figure to find theta
Test yourselfThis 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 HypotenuseThe Opposite SideThe Adjacent SideWhen the Angle MovesRecap: Naming the Sides4Finding the Hypotenuse
The Unknown Below the BarHow Long Is the Kite String?A Leg Below the BarIs the Answer Sensible?Recap: The Hypotenuse7Elevation and Depression
Angle of ElevationMeasuring From Eye LevelAngle of DepressionThe Sun's AngleTwo Triangles, One HeightRecap: Looking Up and Down2The Three Ratios
The Sine RatioThe Cosine RatioThe Tangent RatioChoosing the RatioRecap: The Three Ratios