A tree leaned due to storm. The stick with height of 7 meter from its foot was leaned against the tree to make it straight. If the angle of depression at the point of contacting with the stick on the ground is 30°, find the length of the stick.

Question: A tree leaned due to storm. The stick with height of 7 meter from its foot was leaned against the tree to make it straight. If the angle of depression at the point of contacting with the stick on the ground is 30°, find the length of the stick.

Solution:


মনে করি,
খুঁটিটির দৈর্ঘ্য BC = x মিটার,
গাছের গোড়া থেকে AB = 7 মিটার উচ্চতায় খুঁটিটি ঠেস দিয়ে আছে এবং অবনতি ∠DBC = 30°
∠ACB = ∠DBC = 30° [একান্তর কোণ বলে]

সমকোণী ΔABC থেকে পাই,
sin∠ACB = AB/BC
বা, sin30° = 7/x
বা, 1/2 = 7/x
∴ x = 14

∴ খুঁটিটির দৈর্ঘ্য 14 মিটার।