Q2. A building is 20 meters tall. If the angle of elevation from a point on the ground 10 meters away from the base of the building is θ, what is tan(θ)?
Solution:
tan(θ) = opposite/adjacent = 20/10 = 2.
⏱ Time: 0s
Q3. 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
Q4. 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?
Q5. 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?
Q6. 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?
Q7. A person standing 30 meters away from a building observes the top of the building at an angle of elevation of 60 degrees. How tall is the building?
Q8. 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
Q9. A tree casts a shadow of 15 meters when the angle of elevation of the sun is 30 degrees. How tall is the tree?
Q10. A kite is flying at a height of 40 meters. If the angle of elevation from a point on the ground to the kite is 60 degrees, how far is the point from the base of the kite?
