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Some Applications of Trigonometry MATHS - Some Applications of Trigonometry

UP Board (UPMSP) - STD 10 - MATHS (UPMSP - English Medium). 92 questions in this chapter.

Question types

Some Applications of Trigonometry question types

92 questions across 5 question groups — pick any mix to generate a MATHS paper with step-by-step answer keys.

92
Questions
5
Question groups
5
Question types
Sample Questions

Some Applications of Trigonometry questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1M.C.Q (1 Marks)1 Mark
From a light house the angles of depression of two ships on opposite sides of the light house are observed to be $30^\circ$ and $45^\circ$ . If the height of the light house is $h$ metres, the distance between the ships is :
  • ✓
    $(\sqrt{3}+1)\text{h meters}$
  • B
    $(\sqrt{3}-1)\text{h meters}$
  • C
    $\sqrt{3}\text{h meters}$
  • D
    $1+\Big(1+\frac{1}{\sqrt{3}}\Big)\text{h meters}$

Answer: A.

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Q 2M.C.Q (1 Marks)1 Mark
If the angle of elevation of a tower from a distance of 100 metres from its foot is 60°, then the height of the tower is:
  • ✓
    $100\sqrt{3}\text{m}$
  • B
    $\frac{100}{\sqrt{3}}\text{m}$
  • C
    $50\sqrt{3}$
  • D
    $\frac{200}{\sqrt{3}}\text{m}$

Answer: A.

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Q 3M.C.Q (1 Marks)1 Mark
Two persons are a metres apart and the height of one is double that of the other. If from the middle point of the line joining their feet, an observer finds the angular elevation of their tops to be complementary, then the height of the shorter post is:
  • A
    $\frac{\text{a}}{4}$
  • B
    $\frac{\text{a}}{\sqrt{2}}$
  • C
    $\text{a}\sqrt{2}$
  • ✓
    $\frac{\text{a}}{2\sqrt{2}}$

Answer: D.

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Q 52 Marks Questions2 Marks
B is a pole of height 6m standing at a point B and CD is a ladder inclined at angle of 60° to the horizontal and reaches upto a point D of pole. If AD = 2.54m, find the length of the ladder. $(\text{Use }\sqrt{3}=1.73)$
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Q 62 Marks Questions2 Marks
An observer, 1.5m tall, is 28.5m away from a 30m high tower. Determine the angle of elevation of the top of the tower from the eye of the observer.
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Q 72 Marks Questions2 Marks
An observer, 1.7m tall, is $20\sqrt{3}\text{m}$ away from a tower. The angle of elevation from the eye of an observer to the top of tower is 30°. Find the height of the tower.
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Q 103 Marks Question3 Marks
As observed from the top of a 75m tall light house, the angle of depression of two ships are 30° and 45°. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships.
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Q 113 Marks Question3 Marks
From a point on the ground, 20m away from the foot of a vertical tower, the angle elevation of the top of the tower is 60°, What is the height of the tower?
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Q 123 Marks Question3 Marks
The angles of elevation of the top of a rock from the top and foot of a 100m high tower are respectively 30° and 45°. Find the height of the rock.
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Q 133 Marks Question3 Marks
A kite is flying at a height of 75 metres from the ground level, attached to a string inclined at 60 to the horizontal. Find the length of the string to the nearest metre.
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Q 145 Marks Questions5 Marks
The angle of elevation of a stationery cloud from a point 2500m above a lake is 15° and the angle of depression of its reflection in the lake is 45°. What is the height of the cloud above the lake level? (Use tan 15° = 0.268)
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Q 155 Marks Questions5 Marks
If the angle of elevation of a cloud from a point h metres above a lake is a and the angle of depression of its reflection in the lake be b, prove that the distance of the cloud from the point of observation is, $\frac{2\text{h}\sec\alpha}{\tan\beta-\tan\alpha}.$
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Q 165 Marks Questions5 Marks
A fire in a building B is reported on telephone to two fire stations P and Q, 20km a part from each other on a straight road. P observes that the fire is at an angle of 60° to the road and Q observes that it is at an angle of 45° to the road. Which station should send its team and how much will this team have to travel?
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Q 175 Marks Questions5 Marks
A tree standing on a horizontal plane is leaning towards east. At two points situated at distances a and b exactly due west on it, the angles of elevation of the top are respectively $\alpha$ and $\beta.$ Prove that the height of the top from the ground is, $\frac{(\text{b}-\text{a})\tan\alpha\tan\beta}{\tan\alpha-\tan\beta}.$
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Q 185 Marks Questions5 Marks
PQ is a post of given height a, and AB is a tower at some distance. If $\alpha$ and $\beta$ are the angles of elevation of B, the top of the tower, at P and Q respectively. Find the height of the tower and its distance from the post.
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Q 19Case study (4 Marks)4 Marks
The angle of elevation of a tower from a point on the same level as the foot of the tower is 30°. On advancing 150 metres towards the foot of the tower, the angle of elevation of the tower becomes 60°. Show that the height of the tower is 129.9 metres. $(\text{Use }\sqrt{3}=1.7323=1.732)$
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Q 20Case study (4 Marks)4 Marks
A man on the deck of a ship is 10m above the water level. He observes that the angle of elevation of the top of a cliff is 45° and the angle of depression of the base is 30°. Calculate the distance of the cliff from the ship and the height of the cliff.
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Q 22Case study (4 Marks)4 Marks
There are two temples, one on each bank of a river, just opposite to each other. One temple is 50m high. From the top of this temple, the angles of depression of the top and the foot of the other temple are 30° and 60° respectively. Find the width of the river and the height of the other temple.
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Q 23Case study (4 Marks)4 Marks
From an aeroplane vertically above a straight horizontal road, the angles of depression of two consecutive mile stones on opposite sides of the aeroplane are observed to be $\alpha$ and $\beta.$ Show that the height in miles of aeroplane above the road is given by, $\frac{\tan\alpha\tan\beta}{\tan\alpha+\tan\beta}.$
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