Q. From a point A, the angle of elevation of the top of a building is 45 degrees. If the height of the building is 20 meters, how far is point A from the base of the building?
A.10 m
B.20 m
C.30 m
D.40 m
Solution
Using tan(45°) = height/distance, we have 1 = 20/distance. Therefore, distance = 20 m.
Q. From a point on the ground, the angle of elevation of the top of a hill is 30 degrees. If the distance from the point to the base of the hill is 100 meters, what is the height of the hill?
A.50 m
B.60 m
C.70 m
D.80 m
Solution
Using tan(30°) = height/100, we have 1/√3 = height/100. Therefore, height = 100/√3 ≈ 57.74 m.
Q. From a point on the ground, the angle of elevation of the top of a hill is 30 degrees. If the height of the hill is 50 meters, how far is the point from the base of the hill?
A.50 m
B.75 m
C.100 m
D.125 m
Solution
Using tan(30°) = height/distance, we have 1/√3 = 50/distance. Therefore, distance = 50√3 ≈ 86.6 m.
Q. From a point on the ground, the angle of elevation to the top of a 40 m high building is 45 degrees. How far is the point from the base of the building?
A.40 m
B.20 m
C.30 m
D.50 m
Solution
Using tan(45°) = height/distance, we have distance = height/tan(45°) = 40/1 = 40 m.
Q. From a point on the ground, the angle of elevation to the top of a building is 45 degrees. If the building is 50 meters tall, how far is the point from the base of the building?
Q. From a point on the ground, the angle of elevation to the top of a hill is 30 degrees. If the distance from the point to the base of the hill is 100 meters, what is the height of the hill?
A.100√3 m
B.50 m
C.100 m
D.50√3 m
Solution
Using tan(30°) = height/distance, we have height = distance * tan(30°) = 100 * (1/√3) = 100/√3 = 50 m.
Q. From a point on the ground, the angle of elevation to the top of a hill is 45 degrees. If the height of the hill is 40 m, how far is the point from the base of the hill?
A.20 m
B.40 m
C.60 m
D.80 m
Solution
Using tan(45°) = height/distance, we have 1 = 40/distance. Therefore, distance = 40 m.
Q. From a point on the ground, the angle of elevation to the top of a hill is 45 degrees. If the height of the hill is 20 m, how far is the point from the base of the hill?
A.20 m
B.10 m
C.30 m
D.40 m
Solution
Using tan(45°) = height/distance, we have 1 = 20/distance. Therefore, distance = 20 m.
Q. From a point on the ground, the angle of elevation to the top of a hill is 45 degrees. If the height of the hill is 50 m, how far is the point from the base of the hill?
A.25 m
B.50 m
C.70 m
D.100 m
Solution
Using tan(45°) = height/distance, we have 1 = 50/distance. Therefore, distance = 50 m.
Q. From a point on the ground, the angle of elevation to the top of a hill is 45 degrees. If the height of the hill is 100 m, how far is the point from the base of the hill?
A.100 m
B.50 m
C.200 m
D.150 m
Solution
Using tan(45°) = height/distance, we have distance = height/tan(45°) = 100/1 = 100 m.
Q. From a point on the ground, the angle of elevation to the top of a hill is 45 degrees. If the point is 100 meters away from the base of the hill, what is the height of the hill?
Q. From a point on the ground, the angle of elevation to the top of a tower is 60 degrees. If the tower is 30 m high, how far is the point from the base of the tower?
A.15 m
B.30 m
C.20 m
D.10 m
Solution
Using tan(60°) = height/distance, we have √3 = 30/distance. Therefore, distance = 30/√3 m.
Q. From the top of a 20-meter high building, the angle of depression to a car parked on the ground is 60 degrees. How far is the car from the base of the building?
Q. From the top of a 50 m high building, the angle of depression to a point on the ground is 45 degrees. How far is the point from the base of the building?
A.25 m
B.50 m
C.70 m
D.100 m
Solution
Using tan(45°) = height/distance, we have 1 = 50/distance. Therefore, distance = 50 m.
Q. From the top of a 50-meter high building, the angle of depression to a point on the ground is 45 degrees. How far is the point from the base of the building?
Q. From the top of a 60 m high building, the angle of depression to a point on the ground is 30 degrees. How far is the point from the base of the building?
A.60√3 m
B.30√3 m
C.60 m
D.30 m
Solution
Using tan(30°) = height/distance, we have distance = height/tan(30°) = 60/√3 = 60√3 m.
Q. If a person is standing 50 meters away from a building and the angle of elevation to the top of the building is 60 degrees, what is the height of the building?
