Angle of Elevation

Part of the Right-Triangle Trigonometry section of Coddy's Trigonometry journey. Lesson 30 of 46.

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.

$A cliff of height h seen at 28° from a point 150 m from its foot$

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 $\tan\left(28^{\circ}\right) = \frac{h}{150}$ and $h = 150\tan\left(28^{\circ}\right)$ , 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

$Use the figure to find h$