Trigonometry Height and Distance

Study Material (PDF)
Self Assesment
Study Material (PDF)
Self Assesment

Click on each question to see answer & solution.

Question No: #11

From a point on the roof a house of 11 meters height, it is observed that the angles of depression of the top and foot of a lamp post are 30° and 60° respectively. Find the height of the lamp post.
Ans: 7.34 m
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Question No: #12

From the roof of a five-storey building of 18 meters high, the angle of elevation of the top of the monument is 45° and the angle of depression at the foot of the monument is 60°. Find the height of the monument? [√3 = 1.732]
Ans: 28.392 m (approx)
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Question No: #13

A tower subtends an angle `\alpha` at a point A in the plane of its base and the angle of depression of the foot of the tower at a point `h` meters just above A is `\beta`. Prove that the height of the tower is `h . tan \alpha . cot \beta` meters.

Question No: #14

A boy standing in the middle of a field, observes a flying bird in the north at an angle of elevation of 30° and after 2 minutes, he observes the same bird in the south at an angle of elevation of 60°. If the bird flies all along in a straight line at a height of 50√3 m, then find its speed in km/h.
Ans: 6 km/hr
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Question No: #15

A man standing on a railway overbridge of 5√3 m height observed the engine of the train from one side of the bridge at an angle of depression of 30°. But just after 2 seconds, he observed the engine at an angle of depression of 45° from the other side of the bridge. Find the speed of the train in m/s unit.
Ans: 11.83 m/s
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Question No: #16

An aeroplane is flying parallel to the road at an altitude of 3000 meters at a speed of 100√3 m/s over a straight road. From a point on the road, a man first saw the aeroplane at an angle of elevation 60° to its left and then at an angle of elevation 30° on its right. What is the time difference between those two observations?
Ans: 40 sec
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Question No: #17

A passenger of an airplane observes that Howrah station is at one side of the plane and Saheed Minar is just on the opposite side. The angles of depression of Howrah station and Saheed Minar from the passenger of airplane are 60° and 30° respectively. If the airplane is at a height of 545√3 meters at that time, let us find the distance between Howrah station and Saheed Minar.​
Ans: 2180 m
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Question No: #18

If the angle of depression of two consecutive kilometer stones on a road from an airplane are 60° and 30° respectively. Find the height of the airplane, (i) when the two kilometer stones stand on opposite side of the airplane, (ii) when the two stones stand on the same side of the airplane.
Ans: (i) 250√3 meters, (ii) 500√3 meters.
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Question No: #19

From an aeroplane vertically above a straight horizontal road, the angles of depression of two consecutive kilometer stones on opposite sides of the aeroplane are observed to be `\alpha` and `\beta`. Show that the height of aeroplane above the road is `\frac{tan\alpha tan\beta}{tan\alpha + tan\beta}` km.

Question No: #20

The elevation angles of a light post from two points on the same horizontal line are `\theta` and `\phi` respectively. If the height of the light post is `h` unit and the two points are located on opposite sides of the light post, prove that the distance between the two points is `h(cot \theta + cot \phi)` unit.