Angle of Elevation
Part of the Right-Triangle Trigonometry section of Coddy's Trigonometry journey. Lesson 34 of 50.
Look up at something from level ground. The angle between the horizontal and your line of sight is the angle of elevation. The ground, the object standing upright on it and your line of sight make a right triangle, with the right angle at the foot of the object.
From 150 m away the top of a cliff is at 28° above the horizontal. The height is opposite 28° and the 150 m is adjacent, so tan(28°) = h/150 and h = 150tan(28°), about 79.76 m. Elevation problems with a distance along the ground are tangent problems: the hypotenuse, your line of sight, is rarely what you know.
Challenge
From a boat 120 m from the foot of a lighthouse, the top of the lighthouse is at an angle of elevation of 23°. Find its height h to two decimal places. Then press Check.
Try it yourself
Use the figure to find h
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