Geometry / Unit 9: Right Triangles and Trigonometry
9.7 Angles of Elevation and Depression
Notes
- The angle of elevation is measured up from the horizontal to an object.
- The angle of depression is measured down from the horizontal to an object.
- The angle of elevation from $A$ to $B$ equals the angle of depression from $B$ to $A$ (alternate interior angles).
- Draw the right triangle, label the known parts, and pick the trig ratio.
- Example: 30 m from a tree, the angle of elevation to the top is $40^\circ$. Height $= 30 \tan 40^\circ \approx 25.2$ m.
Practice
You stand 50 feet from a building. The angle of elevation to the top is $40^\circ$. How tall is the building, to the nearest tenth? ($\tan 40^\circ \approx 0.8391$)
Height $= 50 \tan 40^\circ \approx 41.96$.
From the top of a 120-foot lighthouse, the angle of depression to a boat is $20^\circ$. How far is the boat from the base, to the nearest tenth? ($\tan 20^\circ \approx 0.3640$)
The angle at the boat is also $20^\circ$, so $\displaystyle \tan 20^\circ = \frac{120}{d}$ and $\displaystyle d = \frac{120}{\tan 20^\circ} \approx 329.7$.
The angle of elevation from a boat to a cliff top is $25^\circ$. What is the angle of depression from the cliff top to the boat?
They are alternate interior angles between horizontal lines, so they are equal.
Ready for more? Take the Unit 9 test.