web analytics

Ex 9.1, 13 - As observed from top of a 75 m high lighthouse - Ex 9.1

  1. Chapter 9 Class 10 Some Applications of Trigonometry
  2. Serial order wise
Ask Download

Transcript

Ex 9.1 , 13 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. Given that height of the lighthouse is 75 m Hence, AD = 75 m And angle of depression of first ship is 45° So, ∠ PAC = 45 ° And angle of depression of second ship is 30° So, ∠ PAB = 30 ° We need to find distance between the two ships, i.e. BC Now, Lines PA & BD are parallel And AB is the transversal ∴ ∠ ABD = ∠ PAB So, ∠ ABD = 30° Similarly, Line PA & BD are parallel And AC is the transversal ∴ ∠ ACD = ∠ PAC So, ∠ ACD = 45° Since lighthouse is perpendicular to ground ∠ ADB = 90° In right angled triangle ACD, tan C = (𝑆𝑖𝑑𝑒 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑡𝑜 𝑎𝑛𝑔𝑙𝑒" " 𝐶)/(𝑆𝑖𝑑𝑒 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑡𝑜 𝑎𝑛𝑔𝑙𝑒" " 𝐶) tan 45° = 𝐴𝐷/𝐶𝐷 1 = (" " 75)/𝐶𝐷 CD = 75m Similarly, In a right angle triangle ABD, tan B = (𝑆𝑖𝑑𝑒 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑡𝑜 𝑎𝑛𝑔𝑙𝑒" " 𝐵)/(𝑆𝑖𝑑𝑒 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑡𝑜 𝑎𝑛𝑔𝑙𝑒" " 𝐵) tan 30° = 𝐴𝐷/𝐵𝐷 (" " 1)/√3 = (" " 75)/𝐵𝐷 BD = 75√3 BC + CD = 75 √3 BC + 75 = 75 √3 BC = 75 √3 – 75 BC = 75(√3 – 1) m Hence, the distance between two ships = 75(√3 – 1)m

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
  • Gurjeet Singh Thind Singhe's image
    Gurjeet Singh Thind Singhe
    Nov. 14, 2017, 6:57 p.m.
    from the top of a lighthouse the angle of depression of two ships on opposite side of it they are observed to be 30 angle and 90 angle if the hight of the lighthouse is h meters and the line joining the ships passes through the foot of the lighthouse show that the distance between the ships is 4 upon root 3h metres 
    View answer
Jail