Measuring From Eye Level
Part of the Right-Triangle Trigonometry section of Coddy's Trigonometry journey. Lesson 35 of 50.
An angle of elevation is measured at the eye, not at the feet. Your eye is about 1.5 m above the ground, so the right triangle sits on a level line through your eye, and the triangle's height is only the part of the building above that line.
From 12 m away, with your eye 1.5 m up, the top of a wall is at 40°. The part above your eye is h - 1.5, so tan(40°) = (h - 1.5)/12. Multiply by 12 and add 1.5: h = 12tan(40°) + 1.5, about 11.57 m. Forgetting the eye height would give 10.07 m, short by exactly 1.5.
Challenge
Your eye is 1.6 m above the ground, 25 m from a building. The top of the building is at an angle of elevation of 31°. Find the height h of the building 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