9. Some Applications of Trigonometry

Trigonometry

Chapter 9. SOME APPLICATION OF TRIGONOMETRY

Class 10 Maths Chapter 9 Some Application of Trigonometry : Multiple Choice Questions , Answer following the Questions , Fill in the blanks , 2 Marks Questions , 3 Marks Question , 4 Marks Question and Solutions :

Class 10 Some Application Of Trigonometry Multiple Choice Questions and Solutions :

SECTION = A

Q1. The shadow of a 30 m high tower on the ground at some time of the day is m long , then the angle of elevation of the sun at that time is :

(A) 30° (B) 90° (C) 45° (D) 60°

Solution : (d) 60° .

[ Here , m , m

In we have ,

]

Q2. The ratio of the height of a tower and the length of its shadow on the ground is , then the angle of elevation of the sun is : [CBSE2017]

(a) 60° (b) 30° (c) 70° (d) 90°

Solution: (a) 60°

[ Here ,

In we have ,

Therefore, the angle of elevation of the sun is 60° . ]

Q3. The angle of the elevation of the top of a tower from a point on the ground ,which is 15m away from the foot of the tower, is 60° . The height of the tower is :[SEBA 2019]

(a) 15 m (b) m (c) m (d) m

Solution: (b) m

[ Here, m and

In we have ,

Therefore, the height of the tower is m ]

Q4. 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 45° . The height of the tower is : [SEBA 2018]

(a) 30 m (b) 15 m (c) 10 m (d) 60 m

Solution: (a) 30 m

[ Here, m and

In we have ,

Therefore, the height of the tower is 30 m . ]

Q5. A pole casts a shadow of length m on the ground , when the sun’s elevation is 60° then the height of the pole is : [CBSE2015]

(a) 6 m (b) 8 m (c) 12 m (d) 10 m

Solution: (A) 6 m

[ Here , and m

In we have ,

Therefore, the height of the pole is 6 m . ]

Q6. A ladder 15 m long makes an angle of 60° with the wall , then the height of the point where the ladder touches the wall is :

(a) m (b) m (c) m (d) m

Solution: (d) m

[ Here , and m

In we have ,

Therefore, the height of the pole is m .

Q7. In figure, AB is a 6 m high pole and CD is a ladder inclined at an angle of 60° to the horizontal and reaches up to a point D of pole . If AD = 2.54 m , then the length of the ladder is ( Use ) : [CBSE2016]

(a) 3 m (b) 2 m (c) 4 m (d) 8 m

Solution: (c) 4 m

[ Here , m , m , m and

In we have ,

Therefore, the length of the ladder is 4 m . ]

Q8. A ladder of length m reaches a window 15 m high , then the inclination of the ladder with the ground is :

(a) 30° (b) 45° (c) 60° (d) 90°

Solution: (b) 45° .

[ Here , m and m

In we have

Therefore, the inclination of the ladder with the ground is 45° . ]

Q9. The angle of depression of an object from the top of a tower of height 75 m is 30° .Then the distance of the object from the foot of the tower is : [SEBA 2017]

(a) m (b) m (c) m (d) 150 m

Solution: [ ]

Q10. If the angle of elevation of the sun is 45° , then the ratio between the tower and its shadow is : [ SEBA 2015 ]

(a) (b) (c) (d)

Solution: (a) 1 : 1

[ let the height of the tower , the height of shadow and

In we have ,

Therefore, the ratio between the tower and its shadow is 1 : 1 . ]

Q11. When the sun is 30° above the horizontal the length of the shadow cast by 50 m building is :

(a) m (b) m (c) m (d) m

Solution: (b) m

[ Here , and m

In we have ,

Therefore, the length of the building is m. ]

Q12. A ladder , leaning against a wall, makes an angle of 60° with the horizontal . If the foot of the ladder is 2.5 m away from the wall, then the length of the ladder is :

(a) 2.5 m (b) 5.2 m (c) m (d) 5 m

Solution: (d) 5 m

[ Here , m and

In we have ,

Therefore , the length of the ladder is 5 m . ]

Q13. In figure, a tower AB is 20 m high and BC, its shadow on the ground , is m long , then the sun’s altitude is :

(a) 30° (b) 45° (c) 60° (d) 90°

Solution: (a) 30°

[ Here , m and m

In , we have

]

Q14. A tower stands vertically on the ground . From a point on the ground, which is 15 m away from the foot the tower, the angle of elevation of the top of the tower is found to be 30° . The height of the tower is : [SEBA 2020]

(a) m (b) m (c) 15 m (d) m

Solution: (d) m

[ Here , m and

In we have ,

Therefore, the height of the tower is m ]

Class 10 Some Application Of Trigonometry Filled in the blanks

Q1. When an observer see an object situated in upward direction, the angle formed by line of sight with horizontal line is called angled of .

Solution: The angle of elevation .

Q2. When an observer see an object situated in downward direction, the angle formed by line of sight with horizontal line is called angled of .

Solution: The angle of depression .

Q3. The angle of elevation of the sun’s altitude when the height of the shadow of a vertical pole is equal to its height is .

Solution: 45°

[ Here , the height of the shadow and the height of the pole .

Given ,

In we have ,

Therefore, the angle of elevation is 45° . ]

Class 10 Some Application Of Trigonometry Answers following the questions :

Q1. In figure, the angle of elevation of the top of a tower AC from a point B on the ground is 60° . If the height of the tower is 20 m , find the distance of the point from the foot of the tower . [ CBSE 2020 Basic]

Solution: Here, m ,

and the distance of the point from the foot of the tower .

In we have ,

Therefore, the distance of the point from the foot of the tower is m .

Q2. In figure, the angle of elevation of the top of a tower from a point C on the ground, which is 30 m away from the foot of the tower is 30 . Find the height of the tower . [CBSE 2020 standard]

Solution: Here , m ,

And the height of tower .

In we have ,

Therefore, the height of the tower is m .

3. If the height of a vertical pole is times the length of its shadow on the ground, then find the angle of elevation of the sun at that time . [CBSE 2014]

Solution: Given,

In we have ,

Therefore, the angle of elevation of the sun at that time is 60° .

Class 10 Some Application Of Trigonometry 3 Marks Questions and Solutions :

SECTION = C

Q1. The shadow of a tower standing on a level ground is found to be 40 m longer when the sun's altiitude is 30° than when it is 60° . Find the height of the tower .

Solution: In figure, The height of the tower = AB , CD = 40 m ,

Angle of elevation , ADB = 30° and ACB = 60° ..

In ∆ABD we have ,

In ∆ABC we have ,

From (i) and (ii) , we get

From (ii) we get ,

Therefore, height of the tower is .

Q2. From the top of a 7 m high building , the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foot is 45° . Determine the height of the tower .

Solution: In figure , Here, height of the building m ;

the distance between tower and building ;

and

we have ,

In we have ,

From and we get ,

Therefore, the height of the tower is .

Q3. The angle of elevation of the top of a building from the foot of the tower is 30° and the angle of elevation of the top of the tower from the foot of the building is 60° . If the tower is 50 m high, find the height of the building .

Solution:

Q4. A statue , 1.6 m tall, stands on the top of a pedestal. From a point on te ground, the angle of elevation of the top of the statue is 60° and from the same point the angle of elevation of the top of the pedestal is 45° . Find the height of the pedestal .

Class 10 Some Application Of Trigonometry 4 Marks Questions and Solutions :

SECTION = D

Q1. From a balloon vertically above a straight road , the angles of depression of two cars at an instant are found to be 45° and 60° . If the cars are 100 m apart , find the height of the balloon . [Examplar 2020 ]

Solution: let , (= PQ) be the height of the balloon .

In figure , AB = 100 m , PQ =

In , we have

From and , we get

From , we get

Therefore , the height of the balloon is m .

Q2. From a point P on the ground the angle of elevation of the top of a 10 m tall building is 30°. A flag is hoisted at the top of the building and the angle of elevation of the top of the flagstaff from P is 45° .Find the length of the flagstaff and the distance of the building from the point P. [Use 1.73 ]

Solution: In figure, the height of the building m ;

the length of flagstaff .

∴ Angle of elevation are : and

In we have,

m m

Therefore , the distance of the building from the point P is

and the length of the flagstaff is .

Q3. A straight highway leads to the foot of a tower . A man standing at the top of the tower observes a car at an angle of depression of 30°, which is approaching the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be 60°. Find the time taken by the car to reach the foot of the tower from this point.

Solution: let, m ; and [ Speed ]

In we have ,

and we get ,

second

The time taken by the car to reach the foot of the tower is 3 second .