Angles of Elevation and Depression
Angles of elevation and depression describe how steep a line of sight is compared with a horizontal line.
1) Identify the horizontal
- Angle of elevation: measured upward from a horizontal line.
- Angle of depression: measured downward from a horizontal line.
These problems often involve a right triangle, so once you identify the angle and the sides, you can use trigonometric ratios.
2) Draw and label the triangle
- Mark the horizontal line at the observer.
- Place the angle at the correct point: below the horizontal for depression, above it for elevation.
- Label the known side and the unknown side carefully.
3) Choose the trig ratio
Use the ratio that matches the given and needed sides:
- \(\sin = \frac{\text{opposite}}{\text{hypotenuse}}\)
- \(\cos = \frac{\text{adjacent}}{\text{hypotenuse}}\)
- \(\tan = \frac{\text{opposite}}{\text{adjacent}}\)
4) Solve and simplify
Set up the equation, isolate the unknown, and simplify the final answer exactly when possible.
5) Check your result
- Does the angle make sense as an elevation or depression angle?
- Is the answer reasonable compared with the triangle’s shape?
- If you found an angle, does it match the sides you used?
A careful sketch and correct ratio choice are the keys to these problems.