CRE1 - Height & Distance | Geometry - Trigonometry
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There are two, men and a tower in between. The distance between the men is 100 m. The angle of elevation to the top of the tower are 30° and 60° respectively. Find the height of tower.
- (a)
25
- (b)
25√3
- (c)
25/√3
- (d)
None of these
Solution
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ReportA man is standing at some distance from a building. There is a pole at the top of the building. The building subtends an angle of 30° at the man and the angle of elevation of the top of the pole is 45°. Find the height of the pole if the building is 50m high.
- (a)
50(√3 - 1)
- (b)
50√3
- (c)
50/√3
- (d)
None of these
A plane flies above a man at a height of 1000m. The angle of elevation changes from 60° to 30° in 5 sec. Find speed of plane.
- (a)
400(√3 – 1) m/s
- (b)
400√3 m/s
- (c)
400/√3 m/s
- (d)
400/(√3 + 1) m/s
A tree breaks down at some point and touches the ground with the tip making 30° angle with the ground. If the tree is 30 m long; find how high from the ground it broke (in meters).
- (a)
12
- (b)
15
- (c)
20
- (d)
10
A ladder makes 60° with ground when it leans against the wall. The ladder slides down by 5 m along the ground making the angle 45°. Find the length of the ladder.
- (a)
10√2
- (b)
10/(√2 + 1)
- (c)
10/(√2 - 1)
- (d)
10(√2 + 1)
Harsha is riding vertically in a hot air balloon, directly over a point A on the ground. Harsha spots a parked car on the ground at an angle of depression of 30°. The balloon rises 50 meters. Now the angle of depression to the car is 60 degrees. How far is the car from point A?
- (a)
25
- (b)
25√3
- (c)
25/√3
- (d)
None of these
If the shadow of a building increases by 10 meters when the angle of elevation of the sun rays decreases from 60° to 45°, what is the height of the building?
- (a)
10√3
- (b)
10/(√3 - 1)
- (c)
10√3/(√3 + 1)
- (d)
None of these
From the top of a 200 meters high building, the angle of depression to the bottom of a second building is 60 degrees. From the same point, the angle of elevation to the top of the second building is 45 degrees. Calculate the height of the second building.
- (a)
200(√3 + 1)/√3
- (b)
200(√3 + 1)
- (c)
200√3
- (d)
None of these
A plane flies above a man at a height of 1000 m. At one time, angle of elevation is 60°. Suddenly, the plane climbs up at an angle of 30° and 5 seconds later angle of elevation becomes 45°. Speed of plane is?
- (a)
200√3
- (b)
2000/√3
- (c)
400√3
- (d)
400/√3
A man looks up at a pole making angle of elevation is 45°. When he looks at the reflection of the tip of the pole in water, he finds the angle of depression as 60°. If the man is 1 m tall, find height of the pole.
- (a)
1/(3 - 2√3)
- (b)
2 - √3
- (c)
2 + √3
- (d)
None of these