Heights and Distances Applications

⏱ Time: 0s

Q1. From a point on the ground, the angle of elevation to the top of a 15-meter tall building is 45 degrees. How far is the point from the base of the building?

Solution:

Using tan(45°) = height/distance, distance = height/tan(45°) = 15/1 = 15 meters.

⏱ Time: 0s

Q2. If the angle of elevation from a point on the ground to the top of a hill is 30 degrees and the distance from the point to the base of the hill is 20 meters, what is the height of the hill?

Solution:

Using tan(30) = height / 20, height = 20 * tan(30) = 20 * (1/√3) = 20/√3 = 10√3 meters.

⏱ Time: 0s

Q3. A person is standing 12 meters away from a vertical pole. If the angle of elevation to the top of the pole is 45 degrees, what is the height of the pole?

Solution:

Using tan(45) = height / 12, height = 12 * tan(45) = 12 * 1 = 12 meters.

⏱ Time: 0s

Q4. A ladder 25 meters long leans against a wall. If the foot of the ladder is 7 meters from the wall, what is the angle of elevation of the ladder?

Solution:

Using cos(θ) = adjacent/hypotenuse, cos(θ) = 7/25. Therefore, θ = cos⁻¹(7/25) which is approximately 60 degrees.

⏱ Time: 0s

Q5. A 12-meter tall building casts a shadow of 8 meters. What is the angle of elevation of the sun?

Solution:

Using tan(θ) = height/shadow = 12/8 = 1.5, θ = tan⁻¹(1.5) ≈ 36.87 degrees.

⏱ Time: 0s

Q6. From a point on the ground, the angle of elevation to the top of a hill is 45 degrees. If the point is 50 meters away from the base of the hill, what is the height of the hill?

Solution:

Using tan(45°) = height/50, height = 50 * tan(45°) = 50 meters.

⏱ Time: 0s

Q7. A building is 20 meters tall. If the angle of elevation from a point 10 meters away from the base of the building is θ, what is tan(θ)?

Solution:

tan(θ) = height/distance = 20/10 = 2.

⏱ Time: 0s

Q8. If the angle of elevation to the top of a tower from a point 40 meters away is 30 degrees, what is the height of the tower?

Solution:

Using tan(30°) = height/40, height = 40 * (1/√3) = 40/√3 = 20√3 meters.

⏱ Time: 0s

Q9. From a point 30 meters away from the base of a tower, the angle of elevation to the top of the tower is 45 degrees. What is the height of the tower?

Solution:

Using tan(45) = height / 30, we have height = 30 * tan(45) = 30 * 1 = 30 meters.

⏱ Time: 0s

Q10. A person is standing 25 meters away from a vertical pole. If the angle of elevation to the top of the pole is 60 degrees, what is the height of the pole?

Solution:

Using tan(60°) = height/25, height = 25 * √3 = 25√3 meters.

🎉 Test Completed

Total Questions:
Correct:
Wrong:
Accuracy: %
Avg Time / Question: s

📊 View Detailed Performance Back

🎉 Test Completed

On a scale of 0–10, how likely are you to recommend The Soulshift Academy?