Height and Distance - Gujarat Board (GSEB) STD 10 Maths Questions

Q 1M.C.Q (1 Marks)1 Mark

The angle of elevation of the top of a tower from a point on the ground $30m$ away from the foot of the tower is $30^\circ $. The height of the tower is:

A
$30\text{m}$
✓
$10\sqrt{3}\text{m}$
C
$20\text{m}$
D
$10\sqrt{2}\text{m}$

Answer: B.

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Q 2M.C.Q (1 Marks)1 Mark

The tops of two towers of heights $x$ and $y$, standing on a level ground subtend angles of $30^\circ$ and $60^\circ $, respectively at the centre of the line joining their feet. Then, $x : y$ is:

A
$1 : 2$
B
$2 : 1$
✓
$1 : 3$
D
$3 : 1.$

Answer: C.

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Q 3M.C.Q (1 Marks)1 Mark

In a rectangle, the angle between a diagonal and a side is $30^\circ $ and the length of this diagonal is $8cm$. the area of the rectangle is:

A
$16\text{cm}^2$
B
$\frac{16}{\sqrt{3}}\text{cm}^2$
✓
$16\sqrt{3}\text{cm}^2$
D
$8\sqrt{3}\text{cm}^2$

Answer: C.

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Q 4M.C.Q (1 Marks)1 Mark

From the top of a cliff $20m$ high, the angle of elevation of the top of a tower is found to be equal to the angle of depression of the foot of the tower. The height of the tower is:

A
$20m$
✓
$40m$
C
$60m$
D
$80m$

Answer: B.

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Q 5M.C.Q (1 Marks)1 Mark

The string of a kite is $100m$ long and it makes an angle of $60^\circ$ with the horizontal. If these is no slack in the string, the height of the kite from the ground is:

✓
$50\sqrt{3}\text{m}$
B
$100\sqrt{3}\text{m}$
C
$50\sqrt{2}\text{m}$
D
$100\text{m}$

Answer: A.

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Q 61 Marks Question1 Mark

The angle of elevation of the top of a tower from a point on the ground $30m$ away from the foot of the tower is $30^\circ$. The height of the tower is:

A
$30\text{m}$
✓
$10\sqrt{3}\text{m}$
C
$20\text{m}$
D
$10\sqrt{2}\text{m}$

Answer: B.

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Q 71 Marks Question1 Mark

The tops of two towers of heights $x$ and $y$, standing on a level ground subtend angles of $30^\circ$ and $60^\circ$, respectively at the centre of the line joining their feet. Then, $x : y$ is:

A
$1 : 2$
B
$2 : 1$
✓
$1 : 3$
D
$3 : 1$

Answer: C.

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Q 81 Marks Question1 Mark

In a rectangle, the angle between a diagonal and a side is $30^\circ$ and the length of this diagonal is $8\ cm$. the area of the rectangle is:

A
$16\text{cm}^2$
B
$\frac{16}{\sqrt{3}}\text{cm}^2$
✓
$16\sqrt{3}\text{cm}^2$
D
$8\sqrt{3}\text{cm}^2$

Answer: C.

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Q 91 Marks Question1 Mark

From the top of a cliff $20m$ high, the angle of elevation of the top of a tower is found to be equal to the angle of depression of the foot of the tower. The height of the tower is:

A
$20m$
✓
$40m$
C
$60m$
D
$80m$

Answer: B.

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Q 101 Marks Question1 Mark

The string of a kite is $100m$ long and it makes an angle of $60^\circ$ with the horizontal. If these is no slack in the string, the height of the kite from the ground is:

✓
$50\sqrt{3}\text{m}$
B
$100\sqrt{3}\text{m}$
C
$50\sqrt{2}\text{m}$
D
$100\text{m}$

Answer: A.

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Q 113 Marks Question3 Marks

The angle of depression from the top of a tower of a point $A$ on the ground is $30^\circ .$ On moving a distance of $20$ metres from the point $A$ towards the foot of the tower to a point $B,$ the angle of elevation of the top of the tower from the point $B$ is $60^\circ $. Find the height of the tower and its distance from the point $A.$

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Q 123 Marks Question3 Marks

From the top of a tower $100m$ high, a man observes two cars on the opposite sides of the tower and in same straight line with its base, with angles of depression $30^\circ $ and $45^\circ $ respectively. Find the distance between the cars. $\big[\text{Take}\sqrt{3}=1.732\big]$

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Q 133 Marks Question3 Marks

The angles of elevation of the top of a tower from two points at distances of $4\ m$ and $9\ m$ from the base of the tower and in the same straight line with it are complementary. Show that the height of the tower is $6$ metres.

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Q 144 Marks Questions4 Marks

A statue $1.46 \ m$ tall, stands on the top of pedestal. From a point on the ground, the angle of elevation of the top of the statue is $60^{\circ}$ and from the same point, the angle of elevation of the top of the pedestal is $45^{\circ}$. Find the height of the pedestal. $[ Use \sqrt{3}=1.732]$

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Q 154 Marks Questions4 Marks

A vertical tower stands on a horizontal plane and is surmounted by a vertical flagstaff of height 6 m . At a point on the plane, the angle of elevation of the bottom of the flagstaff is $30^{\circ}$ and that of the top of the flagstaff is $60^{\circ}$. Find the height of the tower.
$[ Use \sqrt{3}=1.732]$

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Q 164 Marks Questions4 Marks

From a point on the ground $40 \ m$ away from the foot of a tower, the angle ofclevation of the top of the t wer is $30^{\circ}$. The angle of elevation of the top of a water tank (on the top of the tower) is $45^{\circ}$. Find:

The height of the tower.
The depth of the tank.

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Q 174 Marks Questions4 Marks

A tower stands vertically an the ground.From a point on the ground which is $20\ m$ away from the foot f the tower, th angle of elevation of its top is found tobe $60^\circ $. Find theh ight of the tower. $\big[\text{Take}\sqrt{3}=1.732\big]$

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Q 184 Marks Questions4 Marks

An electrician has to repair an electric fault on a pole of height $4$ metres. He needs to reach a point $1$ metre below the top of the pole to undertake the repair work. What should be the length of the ladder that he should use, which when inclined at an angle of $60^\circ $ to the horizontal would enable him to reach the required position? $\big[\text{Use}\sqrt{3}=1.73\big]$

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Height and Distance question types

Height and Distance questions

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Height and Distance Maths - Height and Distance

Height and Distance question types

Height and Distance questions

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