Pre-Calculus Angles of Elevation and Depression Exam Prep Questions

📚 Quick Study Guide

• 📐 Angle of Elevation: The angle formed by a horizontal line and the line of sight to an object *above* the horizontal line. Imagine looking up at a bird in the sky!
• 📉 Angle of Depression: The angle formed by a horizontal line and the line of sight to an object *below* the horizontal line. Think about looking down from a cliff at a boat.
• 📏 Key Trigonometric Ratios: Remember SOH CAH TOA!
  • sin($\theta$) = Opposite / Hypotenuse
  • cos($\theta$) = Adjacent / Hypotenuse
  • tan($\theta$) = Opposite / Adjacent
• 💡 Problem-Solving Tips:
  • Draw a diagram! Visualizing the problem helps immensely.
  • Identify the right triangle and label the known sides and angles.
  • Choose the appropriate trigonometric ratio based on the given information.
  • Solve for the unknown side or angle.

✍️ Practice Quiz

1. A surveyor stands 100 feet from a building and measures the angle of elevation to the top of the building to be 60°. How tall is the building?
   1. 50 feet
   2. 100$\sqrt{3}$ feet
   3. $\frac{100}{\sqrt{3}}$ feet
   4. 200 feet
2. From the top of a lighthouse 200 feet high, the angle of depression to a boat is 30°. How far is the boat from the base of the lighthouse?
   1. 200$\sqrt{3}$ feet
   2. $\frac{200}{\sqrt{3}}$ feet
   3. 400 feet
   4. 100 feet
3. A ladder leans against a wall, making an angle of 70° with the ground. If the foot of the ladder is 5 feet from the wall, how high up the wall does the ladder reach?
   1. 5tan(70°) feet
   2. 5cos(70°) feet
   3. 5sin(70°) feet
   4. $\frac{5}{tan(70°)}$ feet
4. An airplane is flying at an altitude of 3000 feet. The angle of depression to an airport is 45°. What is the horizontal distance from the airplane to the airport?
   1. 3000 feet
   2. 3000$\sqrt{2}$ feet
   3. $\frac{3000}{\sqrt{2}}$ feet
   4. 6000 feet
5. A person standing on a cliff looks down at a boat. The cliff is 100 meters high, and the angle of depression to the boat is 60°. How far is the boat from the base of the cliff?
   1. $\frac{100}{\sqrt{3}}$ meters
   2. 100$\sqrt{3}$ meters
   3. 200 meters
   4. 50 meters
6. A tower is supported by a wire that reaches from the top of the tower to the ground. The wire is 50 feet long and forms an angle of 65° with the ground. How tall is the tower?
   1. 50sin(65°) feet
   2. 50cos(65°) feet
   3. $\frac{50}{sin(65°)}$ feet
   4. $\frac{50}{cos(65°)}$ feet
7. From a window 30 feet above the ground, the angle of elevation to the top of a nearby building is 40°, and the angle of depression to the base of the building is 20°. How tall is the nearby building?
   1. 30 + 30tan(40°) + 30tan(20°) feet
   2. 30tan(40°) + 30tan(20°) feet
   3. 30tan(40°) - 30tan(20°) feet
   4. 30 + 30cot(40°) + 30cot(20°) feet