Integrated Math 2 / Unit 7: Right Triangle Trigonometry
7.6 Applications
Notes
Angle of elevation is measured up from the horizontal. Angle of depression is measured down from the horizontal. Both equal the angle at the other end by alternate interior angles.
- Draw a right triangle and label the known angle and side.
- Example: standing 50 m from a tree with a $30°$ angle of elevation to the top: height $= 50 \tan 30° \approx 28.9$ m (plus eye height if given).
- Round only at the end.
Practice
You stand 50 m from the base of a tree. The angle of elevation to the top is $30°$. Ignoring eye height, how tall is the tree?
$\displaystyle \tan 30° = \frac{h}{50}$, so $h = 50 \tan 30° \approx 28.9$ m.
A 10 ft ladder makes a $70°$ angle with the ground. How high up the wall does it reach?
The ladder is the hypotenuse and the height is opposite the angle: $10 \sin 70° \approx 9.4$ ft.
From the top of a 40 m lighthouse the angle of depression to a boat is $25°$. How far is the boat from the base of the lighthouse?
The angle at the boat is also $25°$, so $\displaystyle \tan 25° = \frac{40}{d}$ and $\displaystyle d = \frac{40}{\tan 25°} \approx 85.8$ m.
Ready for more? Take the Unit 7 test.