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Heights and Distances Maths - Heights and Distances

Gujarat Board (GSEB) - STD 10 - Maths (GSEB - English Medium). 89 questions in this chapter.

Question types

Heights and Distances question types

89 questions across 3 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.

89
Questions
3
Question groups
5
Question types
Sample Questions

Heights and Distances questions

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

Q 22 Marks Questions2 Marks
$B$ is a pole of height $6m$ standing at a point $B$ and $CD$ is a ladder inclined at angle of $60^\circ$ 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 32 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 42 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 $30^\circ$. Find the height of the tower.
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Q 73 Marks Question3 Marks
As observed from the top of a $75m$ tall light house, the angle of depression of two ships are $30^\circ $ and $45^\circ .$ 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 83 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 $60^\circ ,$ What is the height of the tower$?$
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Q 93 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^\circ $ and $45^\circ .$ Find the height of the rock.
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Q 103 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 114 Marks Questions4 Marks
The angle of elevation of a stationery cloud from a point $2500m$ above a lake is $15^\circ $ and the angle of depression of its reflection in the lake is $45^\circ $. What is the height of the cloud above the lake level? (Use tan $15^\circ = 0.268)$
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Q 124 Marks Questions4 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 134 Marks Questions4 Marks
A fire in a building $B$ is reported on telephone to two fire stations $P$ and $Q, 20 km$ a part from each other on a straight road. $P$ observes that the fire is at an angle of $60^{\circ}$ to the road and $Q$ observes that it is at an angle of $45^{\circ}$ to the road. Which station should send its team and how much will this team have to travel?
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Q 144 Marks Questions4 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 154 Marks Questions4 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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