Question
Download Solution PDFপাহাড়ের উপর থেকে একজন ব্যক্তি একসমান গতিতে তার দিকে এগিয়ে আসা একটি গাড়িকে লক্ষ্য করেন। অবনতি কোণের 45° থেকে 60° তে পরিবর্তিত হতে 10 মিনিট সময় লাগে। এর পরে পাহাড়ের নীচে পৌঁছানোর জন্য গাড়ির দ্বারা গৃহীত প্রয়োজনীয় সময় কত?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCD = 10 একক
Δ ABC-তে
tan 45 = AB/BC
BC = AB --- (1)
ΔABD তে
tan 60 = AB/BD
⇒ √3 = AB/BD
⇒ AB = √3 BD
BC = √3 BD [সমীকরণ (1) থেকে]
BC = BD + CD
⇒ √3 BD – BD = CD
⇒ BD (√3 – 1) = 10
⇒ BD = 10/(√3 – 1) × [(√3 + 1)/(√3 + 1)]
⇒ BD = 10 (√3 + 1)/2
⇒ BD = 5 (1.732 + 1)
⇒ BD = 5 × 2.732
⇒ BD = 13.66 একক
⇒ 10 একক = 10 মিনিট
⇒ 13.66 একক = 13 মিনিট 40 সেকেন্ড
সংক্ষিপ্ত কৌশল:
(√3 – 1) একক = 10 মিনিট
1 একক = 10/(√3 - 1) × [(√3 + 1)/(√3 + 1)]
⇒ 1 একক = 10 (√3 + 1)/2 = 5 (1.732 + 1) = 5 × 2.732 = 13.66
⇒ 13.66 = 13 মিনিট 40 সেকেন্ড
Last updated on Jun 13, 2025
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