Find the distance between the pole and the point.

The angle of elevation of the top of a 30 m long pole, as observed from the point, is 60°.

(Note: Insert any necessary diagram or additional explanation as required.)

Question

19-06-2024
Mathematics

Answered

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Find the distance between the pole and the point.

The angle of elevation of the top of a 30 m long pole, as observed from the point, is 60°.

(Note: Insert any necessary diagram or additional explanation as required.)

Sagot :

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GinnyAnswer GinnyAnswer · Answer 1 · 2024-06-19T22:18:51-04:00

ज़रूर, चलिए इस प्रश्न का विस्तार से हल लिखते हैं:

हमें दिए गए हैं:
- खंभे की ऊँचाई (pole height) = 30 मीटर
- शीर्ष का उठाव कोण (angle of elevation) = 60°

हमसे मांगा गया है:
- खंभे और उस बिंदु के बीच की दूरी (distance between the pole and the point)

चलिए अब इसे हल करते हैं:

1. सबसे पहले, हम यह जानते हैं कि जब कोण दिया गया हो और खंभे की ऊँचाई (ऊर्ध्वाधर उच्चाई) दी गयी हो, तब त्रिकोणमितीय संबंधों का उपयोग करते हुए दूरी (अज्ञात लंबाई) को निकाला जा सकता है।

2. तान (tan) कोण से त्रिकोणमिति का संबंध:
[tex]\[ \text{tan(θ)} = \frac{\text{मुख्य पक्ष (opposite)}}{\text{आधार (adjacent)}} \][/tex]
यहाँ, θ = 60°, मुख्य पक्ष = 30 मीटर, और हमें आधार (distance) ज्ञात करना है।

3. आधार निकालने के लिए हम समीकरण को पुनः व्यवस्थित करते हैं:
[tex]\[ \text{आधार (adjacent)} = \frac{\text{मुख्य पक्ष (opposite)}}{\text{tan(θ)}} \][/tex]

4. कोण 60° के लिए तान (tan) का मान ज्ञात करना आवश्यक है। ज्ञात 60° का तान मान:
[tex]\[ \text{tan}(60°) = \sqrt{3} \][/tex]

5. अब हम मूल्यों को समीकरण में रखते हैं:
[tex]\[ \text{आधार (distance)} = \frac{30}{\sqrt{3}} \][/tex]

6. [tex]\(\sqrt{3}\)[/tex] का मान लगभग 1.732 होता है:
[tex]\[ \text{आधार (distance)} = \frac{30}{1.732} \approx 17.320 \][/tex]

इस प्रकार, हमें खंभे और उस बिंदु के बीच की दूरी लगभग 17.32 मीटर मिलती है।

तो, खंभे की त्रिकोणमितीय गुणों का उपयोग करके यह स्पष्ट होता है कि बिंदु और खंभे के बीच की दूरी 17.32 मीटर है।

Sagot :

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