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Heights and Distances Mathematics - Heights and Distances

ICSE - STD 10 - Mathematics (ICSE - English Medium). 88 questions in this chapter.

Question types

Heights and Distances question types

88 questions across 2 question groups — pick any mix to generate a Mathematics paper with step-by-step answer keys.

88
Questions
2
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 1[5 marks sum]5 Marks
A ladder rests against a wall at an angle $a$, to the horizontal. Its foot is pulled away from the wall through a distance ' $a$ ', so that it slides a distance ' $b$ ' down the wall making an angle $\beta$ with the horizontal. Show that $\frac{a}{b}=\frac{\cos \alpha-\cos \beta}{\sin \beta-\sin \alpha}$.
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Q 2[5 marks sum]5 Marks
From an aeroplane vertically above a straight horizontal road, the angles of depression of two consecutive milestone 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 $\frac{\tan \alpha \tan \beta}{\tan \alpha+\tan \beta}$.
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Q 3[5 marks sum]5 Marks
If the angle of elevation of a cloud from a point $\mathrm{h} \mathrm{m}$ above a lake is $\alpha$, and the angle of depression of its reflection in the lake be $\beta$, prove that distance of the cloud from the point of observation is $\frac{2 \mathrm{~h} \sec \alpha}{\tan \alpha-\tan \beta}$.
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Q 4[5 marks sum]5 Marks
The angle of elevation of the top Q of a vertical tower PQ from a point X on the ground is 60°. At a point Y, 40m vertically above X, the angle of elevation is 45°. Find the height of the tower PQ and the distance XQ.
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Q 5[5 marks sum]5 Marks
The angle of elevation of an aeroplane from a point on the ground is 45°. After 15 seconds, the angle of elevation changes to 30°. If the aeroplane is flying at a height of 3000 m, find the speed of the aeroplane.
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Q 6[4 marks sum]4 Marks
The topmost branch of a tree is tied with a string attached to a pole in the ground. The length of this string Is 200m and it makes an angle of 45° with the ground. Find the distance of the pole to which the string is tied from the base of the tree.
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Q 7[4 marks sum]4 Marks
A kite tied to a string makes an angle of 60° with the ground. Find the perpendicular height of the kite if the length of its string is 250 m.
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Q 8[4 marks sum]4 Marks
An aeroplane takes off at angle of $30^{\circ}$ with the ground. Find the height of the aeroplane above the ground when it has travelled $386 \mathrm{~m}$ without changing direction .
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Q 9[4 marks sum]4 Marks
From the top of a lighthouse, the angles of depression of two ships on the opposite sides of it are observed to be $\alpha$, and $\beta$. If the height of the light house is ' $h$ ' $m$ and the line joining the ships passes through the foot of the light house, show that the distance between the ship is $\frac{\mathrm{h}(\tan \alpha+\tan \beta)}{\tan \alpha \tan \beta} \mathrm{m}$
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Q 10[4 marks sum]4 Marks
$
\text { Find the length of the shadow cast by a tree } 60 \mathrm{~m} \text { high when the sun's altitude is } 30^{\circ} \text {. }
$
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