Trigonometry / Unit 2: Right Triangle Trigonometry
2.5 Angles of Elevation and Depression
Notes
The angle of elevation is measured up from the horizontal to a line of sight. The angle of depression is measured down from the horizontal.
- Draw a right triangle with the horizontal and vertical as the legs.
- The angle of depression from A to B equals the angle of elevation from B to A (alternate interior angles).
- Example: standing 30 m from a tree and looking up at $45^\circ$, the tree is $30\tan 45^\circ = 30$ m taller than eye level.
Practice
You stand 50 m from the base of a tower. The angle of elevation to the top is $40^\circ$. About how tall is the tower above your eye level?
$\displaystyle \tan 40^\circ = \frac{h}{50}$, so $h = 50\tan 40^\circ \approx 42.0$.
From the top of an 80 m cliff, the angle of depression to a boat is $25^\circ$. About how far is the boat from the base of the cliff?
The angle at the boat is also $25^\circ$: $\displaystyle \tan 25^\circ = \frac{80}{d}$, so $\displaystyle d = \frac{80}{\tan 25^\circ} \approx 171.6$.
A pilot sees an airport at an angle of depression of $30^\circ$. What is the angle of elevation from the airport up to the plane?
The horizontals are parallel, so the angles are equal (alternate interior angles).
Ready for more? Take the Unit 2 test.