The line of sight, the angle of elevation and the angle of depression. Drawing a right triangle from a word problem and using one trigonometric ratio to find a height or a distance.
3 lessons, about 1 h 30 min3 simulations10 problems6 practice questionsPython in every lesson
Created by StemPy LabThe line of sight is the straight line from your eye to the object you look at. Its angle with the horizontal is the angle of elevation when you look up and the angle of depression when you look down. For the same line of sight, the two angles are equal. To solve a problem, draw a right triangle and pick the ratio that uses the two sides you need.
To find the height of a tower, tree or pole from the angle of elevation and the distance from its foot, use the tangent. The height is the distance times tan of the angle. If the eye is above the ground, add the eye height. When you know the slanting length, such as a kite string, use the sine.
To find a ground distance from a height and an angle, divide the height by the tangent. A ladder of length L at an angle with the ground reaches a height L sin and has its foot L cos from the wall. A shadow is the height divided by tan of the sun's altitude. To find the angle itself, find its tangent and use the inverse tangent.
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