Q. A kite is flying at a height of 30 m. 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?
A.15√3 m
B.30 m
C.10√3 m
D.20 m
Solution
Using tan(60°) = height/distance, we have distance = height/tan(60°) = 30/√3 = 15√3 m.
Q. A kite is flying at a height of 30 meters. If the angle of elevation from a point on the ground to the kite is 45 degrees, how far is the point from the base of the kite?
A.15 m
B.30 m
C.45 m
D.60 m
Solution
Using tan(45°) = height/distance, we have 1 = 30/distance. Therefore, distance = 30 m.
Q. A kite is flying at a height of 50 meters. If the angle of elevation from a point on the ground to the kite is 30 degrees, how far is the point from the base of the kite?
Q. A ladder is leaning against a wall. The foot of the ladder is 12 meters away from the wall, and the angle between the ladder and the ground is 60 degrees. What is the height at which the ladder touches the wall?
A.12√3 m
B.6 m
C.12 m
D.24 m
Solution
Using sin(60°) = height/hypotenuse, we find the height = 12 * tan(60°) = 12√3 m.
Q. A man is standing 100 meters away from a building. If the angle of elevation to the top of the building is 45 degrees, what is the height of the building?
A.100 m
B.50 m
C.75 m
D.25 m
Solution
Using tan(45°) = height/distance, we have height = distance * tan(45°) = 100 * 1 = 100 m.
Q. A man is standing 30 meters away from a tower. If the angle of elevation of the top of the tower from the man's position is 30 degrees, what is the height of the tower?
Q. A man is standing 30 meters away from a tree. If the angle of elevation from his eyes to the top of the tree is 30 degrees, what is the height of the tree?
Q. A man is standing 30 meters away from a tree. If the angle of elevation of the top of the tree from his eyes is 60 degrees, what is the height of the tree?
Q. A man is standing 40 meters away from a building. If the angle of elevation to the top of the building is 30 degrees, what is the height of the building?
Q. A man is standing 50 meters away from a vertical pole. If he looks up at an angle of elevation of 60 degrees to the top of the pole, what is the height of the pole?
A.25 m
B.30 m
C.35 m
D.40 m
Solution
Using tan(60°) = height/50, we have √3 = height/50. Therefore, height = 50√3 ≈ 86.6 m.
Q. A man is standing on a hill 80 meters high. If he looks at a point on the ground at an angle of depression of 45 degrees, how far is the point from the base of the hill?
Q. A man is standing on the ground and looking at the top of a 15 m high pole. If he is 20 m away from the base of the pole, what is the angle of elevation?
A.36.87 degrees
B.45 degrees
C.60 degrees
D.30 degrees
Solution
Using tan(θ) = height/distance, we have tan(θ) = 15/20. Therefore, θ = tan⁻¹(0.75) which is approximately 36.87 degrees.
Q. A man is standing on the ground and looking at the top of a 40 m high building. If the angle of elevation is 60 degrees, how far is he from the building?
A.20 m
B.40 m
C.20√3 m
D.40√3 m
Solution
Using tan(60°) = height/distance, we have distance = height/tan(60°) = 40/√3 = 20√3 m.
Q. A man is standing on the ground and looking at the top of a building. If the angle of elevation is 45 degrees and he is 10 meters away from the building, what is the height of the building?
Q. A man is standing on the ground and looking at the top of a tree. If the angle of elevation is 60 degrees and he is 10 meters away from the base of the tree, what is the height of the tree?
A.5√3 m
B.10√3 m
C.15√3 m
D.20√3 m
Solution
Using tan(60°) = height/10, we have √3 = height/10. Therefore, height = 10√3 m.
Q. A man is standing on the ground and observes the top of a building at an angle of elevation of 60 degrees. If he is 50 m away from the building, what is the height of the building?
A.25 m
B.43.3 m
C.50 m
D.86.6 m
Solution
Using tan(60°) = height/50, we have √3 = height/50. Therefore, height = 50√3 ≈ 86.6 m.
Q. A man is standing on the ground and observes the top of a tree at an angle of elevation of 45 degrees. If he is 10 meters away from the tree, what is the height of the tree?
A.5 m
B.10 m
C.15 m
D.20 m
Solution
Using tan(45°) = height/10, we have 1 = height/10. Therefore, height = 10 m.
Q. A person is standing 100 meters away from a building. If the angle of elevation to the top of the building is 45 degrees, what is the height of the building?
A.100 m
B.50 m
C.75 m
D.25 m
Solution
Using tan(45°) = height/distance, we have height = distance * tan(45°) = 100 * 1 = 100 m.
Q. A person is standing 20 meters away from a vertical cliff. If the angle of elevation to the top of the cliff is 60 degrees, what is the height of the cliff?
A.10√3 m
B.20√3 m
C.30√3 m
D.40√3 m
Solution
Using tan(60°) = height/20, we have √3 = height/20. Therefore, height = 20√3 m.
Q. A person is standing 25 meters away from a vertical cliff. If the angle of elevation to the top of the cliff is 60 degrees, what is the height of the cliff?
A.10 m
B.15 m
C.20 m
D.25 m
Solution
Using tan(60°) = height/25, we have √3 = height/25. Therefore, height = 25√3 ≈ 43.3 m.
Q. A person is standing 25 meters away from a vertical pole. If the angle of elevation to the top of the pole is 36.87 degrees, what is the height of the pole?
A.15 m
B.20 m
C.25 m
D.30 m
Solution
Using tan(36.87°) = height/distance, we have height = distance * tan(36.87°) = 25 * 0.75 = 15 m.
Q. A person is standing 30 m away from the base of a tree. If the angle of elevation to the top of the tree is 60 degrees, what is the height of the tree?
A.15 m
B.20 m
C.25 m
D.30 m
Solution
Using tan(60°) = height/30, we have √3 = height/30. Therefore, height = 30√3 = 25 m.
Q. A person is standing 30 m away from the foot of a tree. If the angle of elevation to the top of the tree is 60 degrees, what is the height of the tree?
A.15 m
B.20 m
C.25 m
D.30 m
Solution
Using tan(60°) = height/30, we have √3 = height/30. Therefore, height = 30√3 = 25 m.
Q. A person is standing 30 meters away from the foot of a tree. If the angle of elevation to the top of the tree is 60 degrees, what is the height of the tree?
A.15√3 m
B.30 m
C.30√3 m
D.45 m
Solution
Using tan(60°) = height/distance, we have height = distance * tan(60°) = 30√3 m.
Q. A person is standing 40 m away from a building. If the angle of elevation to the top of the building is 30 degrees, what is the height of the building?
A.20 m
B.40 m
C.30 m
D.10 m
Solution
Using tan(30°) = height/distance, we have height = distance * tan(30°) = 40 * (1/√3) ≈ 20 m.
