Processing math: 1%

CBSE Questions for Class 10 Maths Some Applications Of Trigonometry Quiz 6 - MCQExams.com

The length of a string between a kite and a point on the ground is 90m. The string makes an angle of 60 with the level ground if there is no slack in the string, the height of the kite is 
  • 903m
  • 453m
  • 180m
  • 45m
The angle of elevation of the top of a tower at a distance of \displaystyle \frac{50\sqrt{3}}{3} metres from the foot is \displaystyle 60^{\circ}. Find the height of the tower 
  • \displaystyle 50\sqrt{3} metres
  • \displaystyle \frac{20}{\sqrt{3}} metres
  • -50 metres
  • 50 metres
If from the top of a tower 50 m high, the angles of depression of two objects due north of the tower are respectively \displaystyle 60^{\circ} and \displaystyle 45^{\circ}, then the approximate distance between the objects is :
  • \displaystyle 50\left ( \sqrt{2}-2 \right )m
  • \displaystyle 50\left ( \sqrt{3}-3 \right )m
  • 31 \ m
  • None of these
A man on a cliff observes a boat at an angle of depression of \displaystyle 30^{\circ} which is approaching the shore to the point immediately beneath the observer with a uniform speed. Six minutes later the angle of depression of the boat is found to be \displaystyle 60^{\circ}. Find the total time taken by the boat from the initial point to reach the shore.
  • 9 min
  • 7 min
  • 10 min
  • 6 min
The angle of elevation of the top of tower as observed from a pint on the horizontal ground is 'x' if we move a distance 'd' towards the foot of the tower the angle of elevation increases to 'y' then the height of the tower is 
  • \displaystyle \frac{d\tan x\tan y}{\tan y-\tan x}
  • \displaystyle d(\tan y+\tan x)
  • \displaystyle d(\tan y-\tan x)
  • \displaystyle \frac{d\tan x\tan y}{\tan y+\tan x}
The angels of elevation of the top of a vertical tower from two points 30 meter apart and on the same straight line passing through the base of tower are \displaystyle 30^{\circ} and \displaystyle 60^{\circ} respectively The height of the tower is 
  • 10 m
  • 15 m
  • \displaystyle 15\sqrt{3}m
  • 30 m
The angle of elevation of the top of a tower from a point on the ground \displaystyle 30^{\circ} after walking 200 m towards the tower the angle of elevation becomes \displaystyle 60^{\circ}. The height of the tower is 
  • \displaystyle 100\sqrt{3} m
  • \displaystyle 200\sqrt{3} m
  • 100 m
  • 200 m
The angles of elevation of the top of a vertical tower from two points 30 metres apart and on the same straight line passing through the base of tower are \displaystyle 30^{\circ} and \displaystyle 60^{\circ} respectively. The height of the tower is 
  • 10 m
  • 15 m
  • \displaystyle 15\sqrt{3}m
  • 30 m
If the altitude of the sun is at \displaystyle 60^{\circ} then the height of the vertical tower that will cast a shadow of  length 20 m is 
  • \displaystyle 20\sqrt{3}m
  • \displaystyle \frac{20}{\sqrt{3}}m
  • \displaystyle \frac{15}{\sqrt{3}}m
  • \displaystyle 40\sqrt{3}m
The length of a ladder is exactly equal to the height of the wall it is leaning against. If the lower end of the ladder is kept on a bench of height 3 m. and the bench is kept 9 m. away from the wall, the upper end of the ladder coincides with the top of the wall. The height of the wall is
  • 11 m
  • 12 m
  • 15 m
  • 18 m
The shadow of a tower is 30 meters when the sun's altitude is \displaystyle 30^{\circ}. When the sun's altitude is \displaystyle 60^{\circ} then the length of shadow will be 
  • 60 m
  • 15 m
  • 10 m
  • 5 m
The angle of depression of a car moving with uniform speed towards the building as observed from the top of the building is found to be 30^{\circ}. The same angle of depression changes to 60^{\circ} after 12 seconds. How much more time would the car take to reach the base?
  • 6 sec
  • 8 sec
  • 4 sec
  • 12 sec
The angle of elevation of the top of a building from the foot of the tower is 30 and the angle of the elevation of the top of the tower from the foot of the building is 60. If the tower is 50 m high, then the height of the building is :
  • \displaystyle \frac { 50 }{ 3 } m
  • \displaystyle \frac { 35 }{ 3 } m
  • \displaystyle \frac { 47 }{ 3 } m
  • \displaystyle \frac { 52 }{ 3 } m
 The angles of elevation of the top of a tower from two points a and b from the base and in the same straight line with it are complementary. The height of the tower is :
  • \displaystyle ab
  • \displaystyle \sqrt { ab }
  • \displaystyle { a }^{ 2 }{ b }^{ 2 }
  • None of these
Two poles of equal heights are standing opposite to each other on either side of a road, which is 100 metres wide. From a point between them on the road, the angles of elevation of their tops are 30 and 60. The height of each pole is :
  • 44 m
  • 43.25 m
  • 50 m
  • 40.5 m
The angle of elevation of the top of a tower from a point on the ground, which is 30 m away from the foot of the tower is 30. The height of the tower is :
  • \displaystyle 8\sqrt { 3 } m
  • \displaystyle 9\sqrt { 3 } m
  • \displaystyle 10\sqrt { 3 } m
  • \displaystyle 12\sqrt { 3 } m
The shadow of a vertical tower on level ground increases by 10 metres when the altitude of the sun changes from the angle of elevation 45^0 to 30^0. Find the height of the tower correct to one place of decimal.
(take \displaystyle \sqrt { 3 } =1.732)

348279_e0e4c7324a3741b5a6901305368d1a60.png
  • 13.67\ m
  • 15\ m
  • 18.67\ m
  • 20\ m
A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle 30 with it. The distance between the foot of the tree to the point where the top touches the ground is 8 m. The height of the tree is:
  • \displaystyle 5\sqrt { 3 } m
  • \displaystyle 8\sqrt { 3 } m
  • \displaystyle 10\sqrt { 3 } m
  • \displaystyle 6\sqrt { 3 } m
From the top of a building h metres high, the angle of elevation of a monument is 45^o and angle of depression of its foot is 30^o. The height of the monument is
  • \sqrt 3h
  • \dfrac {(\sqrt 3+1)}{2}h
  • \dfrac {\sqrt 3-1}{2}h
  • (\sqrt 3+1)h
From a point on the ground, the angles of elevation of the bottom and top of a transmission tower fixed at the top of a 20 m high building are 45 and 60 respectively. The height of the tower is:
  • \displaystyle 25\left( \sqrt { 3 } -1 \right)\ m
  • \displaystyle 20\left( \sqrt { 3 } -1 \right)\ m
  • \displaystyle 20\ m
  • \displaystyle 10\ m
A kite is flying at a height of 60 m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is 60. Find the length of the string, assuming that there is no slack in the string. 
  • \displaystyle 40\sqrt { 3 } m
  • \displaystyle 30\sqrt { 3 } m
  • \displaystyle 20\sqrt { 3 } m
  • \displaystyle 10\sqrt { 3 } m
The angle of elevation of the top of a hill at the foot of a tower is 60 and the angle of elevation of top of the tower from the foot of the hill is 30. If the tower is 50 m high, then the height of the hill is :
  • 148 m
  • 150 m
  • 152 m
  • 160 m
The shadow of a pole standing on a horizontal plane is a meters longer when the sun's elevation is \theta than when it is \phi. The height of the pole will be:   {Use \sin(A-B) = \sin A \cos B - \sin B \cos A}
  • a\displaystyle\frac{\cos\theta\cdot\cos\phi}{\cos(\theta-\phi)} meter
  • a\displaystyle\frac{\sin\theta\sin\phi}{\sin(\phi-\theta)} meter
  • a\displaystyle\frac{\sin\theta\cos\phi}{\sin(\theta-\phi)} meter
  • a\displaystyle\frac{\sin\phi\cos\theta}{\cos(\theta-\phi)} meter
From the top of house 32 meter high, if the angle of elevation of the top of a tower is \displaystyle 45^{\circ}  and the angle of depression of the foot of the tower is \displaystyle 30^{\circ} , then the height of the tower is 
  • \displaystyle \frac{32}{\sqrt{3}}(\sqrt{3+1}) meter
  • \displaystyle 32(\sqrt{3+1}) meter
  • \displaystyle 32\sqrt3 meter
  • \displaystyle \frac{32}{3}(\sqrt{3+1}) meter
An aeroplane flying horizontally at a height of 1.5 km above the ground is observed at a certain point on earth to subtend an angle of 60. After 15 seconds, its angle of elevation is observed to be 30. Calculate the speed of the, aeroplane in km/h. 
  • \displaystyle 240\sqrt { 3 } km/h
  • \displaystyle 230\sqrt { 3 } km/h
  • \displaystyle 210 km/h
  • \displaystyle 220  km/h
If the angle of elevation of an object from a point 200 meter above the lake is found to be   \displaystyle 30 ^{\circ} and the angle of  depression of its image in the  lake is  \displaystyle 45^{\circ} , then the height of the object above the lake is 
  • \displaystyle \frac{200\left ( \sqrt{3-1} \right )}{\left ( \sqrt{3+1} \right )} meter
  • \displaystyle \frac{200\left ( \sqrt{3-1} \right )}{\sqrt{3}}
  • \displaystyle \frac{200\left ( \sqrt{3+1} \right )}{\sqrt{3}}
  • \displaystyle \frac{200\left ( \sqrt{3+1} \right )}{\left ( \sqrt{3+1} \right )} meter
A vertical tower stands on a horizontal plane and is surmounted by a vertical flagstaff of height h. At a point on the plane, the angle of elevation of the bottom of the flagstaff is \displaystyle \alpha  and that of the top of the flagstaff is \displaystyle \beta  Then the
height of the tower is :
  • \displaystyle \frac { h }{ \tan { \alpha } }
  • \displaystyle \frac { h\tan { \alpha } }{ \tan { \beta } -\tan { \alpha } }
  • \displaystyle \frac { \tan { \beta } }{ h }
  • \displaystyle \frac { \tan { \alpha } }{ \tan { \beta } -\tan { \alpha } }
The angles of elevations of the top of the tower from two points in the same straight line and at a distance of 9 \text{ m} and 16\text{ m} from the base of the tower are complementary. The height of the tower is :
  • 18\text{ m}
  • 16\text{ m}
  • 10\text{ m}
  • 12\text{ m}
The angle of elevation of the top of a tower at a distance of \displaystyle\frac{50\sqrt{3}}{3} metres from the foot is 60^\circ. Find the height of the tower.
  • 50\sqrt{3}\:m
  • \displaystyle\frac{20}{\sqrt{3}}\:m
  • -50 m
  • 50 m
The angles of elevation of the top of a tower from two points at the distances of 4\ m and 9\ m from the base of the tower and in the same straight line with it are complementary. The height of the tower is :
  • 8\ m
  • 5\ m
  • 6\ m
  • 4\ m
0:0:1


Answered Not Answered Not Visited Correct : 0 Incorrect : 0

Practice Class 10 Maths Quiz Questions and Answers