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Ex 9.1 NCERT Solutions(Part- 1)- Some Applications of Trigonometry Class 10 Notes | EduRev

Class 10 : Ex 9.1 NCERT Solutions(Part- 1)- Some Applications of Trigonometry Class 10 Notes | EduRev

The document Ex 9.1 NCERT Solutions(Part- 1)- Some Applications of Trigonometry Class 10 Notes | EduRev is a part of the Class 10 Course Class 10 Mathematics by VP Classes.
All you need of Class 10 at this link: Class 10

Q.1. A circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with the ground level is 30Â° (see figure).

Sol. Given: length of the rope (AC) = 20 m, âˆ ACB = 30Â°
Let height of the pole (AB) = h metre

â‡’ h/20 = 1/2
â‡’ h = 20/2 = 10 m
Hence, height of the pole = 10 m

Q.2. A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle 30Â° with it. The distance between the foot of the tree to the point where the top touches the ground is 8 m. Find the height of the tree.
Sol. Let DB is a tree and AD is the broken part of it which touches the ground at C.

Given: âˆ ACB = 30Âº
and BC = 8m
Let AB = x m
âˆ´ Now, length of the tree
= (x + y) m
In Î” ABC

â‡’
â‡’       ... (i)

Hence, total height of the tree

Q3. A contractor plans to install two slides for the children to play in a park. For the children below the age of 5 years, she prefers to have a slide whose top is at a height of 1.5 m, and is inclined at an angle of 30Â° to the ground, whereas for older children, she wants to have a steep slide at a height of 3 m, and inclined at an angle of 60Â° to the ground. What should be the length of the slide in each case?
Sol. Let l1 is the length of slide for children below the age of 5 years and l2 is the length of the slide for elder children.

In Î”ABC

Q.4. 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 30Â°. Find the height of the tower.
Sol. Let h be the height of the tower

â‡’
â‡’

Q.5. 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 60Â°. Find the length of the string, assuming that there is no slack in the string.
Sol. Given: height AB = 60 m, âˆ ACB = 60Â°, AC = length of the string

Hence, length of the string = 40âˆš3 m

Q.6. A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angle of elevation from his eyes to the top of the building increases from 30Â° to 60Â° as he walks towards the building. Find the distance he walked towards the building.
Sol. Let  AB = height of the building

The distance walked by the boy towards building
DE = DF - EF

Q.7. From a point on the ground, the angles of elevation of the bottom and the top of a transmission tower fixed at the top of a 20 m high building are 45Â° and 60Â° respectively. Find the height of the tower.
Sol. Given: AB = 20 m (Height of the building)
Let AD = h m (Height of the tower)

Hence, height o f the tower =

Q.8. A statue, 1.6 m tall, stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60Â° and from the same point the angle of elevation of the top of the pedestal is 45Â°. Find the height of the pedestal.
Sol. Let the height of the pedestal AB = h m
Given: height of the statue = 1.6 m, âˆ ACB = 45Â° and âˆ DCB = 60Â°

Hence, height of the pedestal

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