SATHEE: Properties of Triangles 3 Question 4

Properties of Triangles 3 Question 4

4. Which of the following pieces of data does not uniquely determine an acute angled $△ A B C$ ( $R$ being the radius of the circumcircle)?

(2002, 1M)

(a) $a, \sin A, \sin B$

(b) $a, b, c$

(d) $a, \sin A, R$

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Answer:

Correct Answer: 4. (d)

Solution:

First solve each option separately.

(a) If $a, \sin A, \sin B$ are given, then we can determine $b = \frac{a}{\sin A} \sin B, c = \frac{a}{\sin A} \sin C$ . So, all the three sides are unique.

So, option (a) is incorrect.

(b) The three sides can uniquely make an acute angled triangle. So, option (b) is incorrect.

(c) If $a, \sin B, R$ are given, then we can determine $b = 2 R \sin B, \sin A = \frac{a \sin B}{b}$ . So, $\sin C$ can be determined.

Hence, side $c$ can also be uniquely determined.

(d) If $a, \sin A, R$ are given, then

$\frac{b}{\sin B} = \frac{c}{\sin C} = 2 R$

But this could not determine the exact values of $b$ and $c$ .

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अगला

Properties of Triangles 3 Question 4

4. Which of the following pieces of data does not uniquely determine an acute angled $△ A B C$ ( $R$ being the radius of the circumcircle)?

Answer:

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

Properties of Triangles 3 Question 4

4. Which of the following pieces of data does not uniquely determine an acute angled △ABC ( R being the radius of the circumcircle)?

Answer:

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

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4. Which of the following pieces of data does not uniquely determine an acute angled $△ A B C$ ( $R$ being the radius of the circumcircle)?