A 30-meter pole has fractured and bent over to make a 30° angle with the ground, remaining partially attached. How high from the base did it break?

Question: A 30-meter pole has fractured and bent over to make a 30° angle with the ground, remaining partially attached. How high from the base did it break?

Solution:

ধরি,
খুটিটি x মিটার উচুতে ভেঙ্গেছিল।
∴ অপর ভাঙ্গা অংশের দৈর্ঘ্য = (30 - x) মিটার

এখন,
sin θ = লম্ব/অতিভুজ
বা, sin θ = x/(30 - x)
বা, sin 30° = x/(30 - x)
বা, 1/2 = x/(30 - x)
বা, 2x = 30 - x
বা, 2x + x = 30
বা, 3x = 30
⇒ x = 10

∴ খুটিটি ভূমি থেকে 10 মিটার উচুতে ভেঙ্গেছিল।