# Class 10 Mathematics Chapter 9: Some Applications of Trigonometry - NCERT Solutions

Welcome to the complete NCERT solutions for Class 10 Mathematics Chapter 9: Some Applications of Trigonometry. In this section, we provide detailed, easy-to-understand solutions for all the questions from this chapter. Whether you're preparing for exams or seeking a deeper understanding of the subject, these Some Applications of Trigonometry question answers will offer you valuable insights and explanations. Each solution is crafted to ensure conceptual clarity and step-by-step problem-solving methods, enabling students to grasp the core themes and excel in their academics.

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### Exercise 1 ( Page No. : 205 )

•  Q1 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 30° (see Fig. 9.11). Ans: Let AB = hm be the height of pole and length of rope is 20 m tied from the          Top of tower AB and = 30o                                                                            In right   Δ ABC, we have Q2 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. Find the height of the tree. Ans: 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, andis inclined at an angle of 30° to the ground, whereas for elder children, she wants to have a steep slide at a height of 3m, and inclined at an angle of 60° to the ground. What should be the length of the slide in each case? Ans: (i) For Children below age of 5 years Height of slide = 1.5 m Angle of inclination of slide = 30o (ii) For Children below age of 5 years Height of slide = 3m Angle of inclination of slide = 60o Draw figure for both cases:          In right Δ ABC, we have Sin 30o  =  AB / AC           =>     1/ 2  = 1.5 /AC                                                      [ sin30o =1/2] AC  =  3m In right Δ DEF, we have Sin 60o  = DE /DF                 =>                                         DF  = 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 30°. Find the height of the tower. Ans: Q5 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. Ans: Draw a figure according  to given conditions, Q6 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 30° to 60° as he walks towards the building. Find the distance he walked towards the building. Ans: Q7 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 45° and 60° respectively. Find the height of the tower. Ans: Let AB = x m be the height of transmission tower          BC = 20 m height of building       (given)          Angle of elevation from top of tower = 600           Angle of elevation from bottom of tower = 45o           To find : height of tower i.e., AB Q8 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 60° and from the same point the angle of elevation of the top of the pedestal is 45°. Find the height of the pedestal. Ans: Q9 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. Ans: Q10 Two poles of equal heights are standing opposite each other on either side of the road, which is 80 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 60° and 30°, respectively. Find the height of the poles and the distances of the point from the poles. Ans: Q11 A TV tower stands vertically on a bank of a canal. From a point on the other bank directly opposite the tower, the angle of elevation of the top of the tower is 60°. From another point 20 m away from this point on the line joing this point to the foot of the tower, the angle of elevation of the top of the tower is 30° (see Fig. 9.12). Find the height of the tower and the width of the canal. Ans: Q12 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. Ans: Q13 As observed from the top of a 75 m high lighthouse from the sea-level, the angles of depression of two ships are 30° and 45°. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships. Ans: Q14 A 1.2 m tall girl spots a balloon moving with the wind in a horizontal line at a height of 88.2 m from the ground. The angle of elevation of the balloon from the eyes of the girl at any instant is 60°. After some time, the angle of elevation reduces to 30° (see Fig. 9.13). Find the distance travelled by the balloon during the interval. Ans: Q15 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. Ans: Q16 The angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line with it are complementary. Prove that the height of the tower is 6 m. Ans: Let the height of tower AB = x m

### Key Features of NCERT Class 10 Mathematics Chapter 'Some Applications of Trigonometry' question answers :

• All chapter question answers with detailed explanations.
• Simple language for easy comprehension.
• Aligned with the latest NCERT guidelines.
• Perfect for exam preparation and revision.