In a - ABC- if sin2 A - sin2 B - sin2 C - 2- then the triangle can be

The correct option is B right angledWe can consider triangle #160;ABC #160;as a #160;right #160;triangle. #160;But #10;most appropriately we can sa ...

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Standard IX

Mathematics

Relationship between Trigonometric Ratios

In a Δ ABC,...

Question

In a $Δ A B C$ , if ${sin}^{2} A + {sin}^{2} B + {sin}^{2} C = 2$ , then the triangle can be

equilateral

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right angled

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Isosceles

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None of these

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Solution

The correct option is B right angled
We can consider triangle ABC as a right triangle. But most appropriately we can say it a right isosceles triangle.

As its terms also satisfy the law:
${sin}^{2} A + {sin}^{2} B + {sin}^{2} C = 2 + 2 cos A . cos B . cos C$

Thus, $2 cos A . cos B . cos C$ can only be diminished if one of them is right angle.

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Similar questions

Q. In

Δ A B C,

{sin}^{2} A + {sin}^{2} B = {sin}^{2} C,

then show that the triangle is a right angled triangle.

Q. In ∆ABC, if sin² A + sin² B = sin² C. show that the triangle is right-angled.

Q. Assertion :Statement 1:If in a triangle

{sin}^{2} A + {sin}^{2} B + s i n^{2} C = 2

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then prove that the triangle is right-angled.

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{sin}^{2} A + {sin}^{2} B + {sin}^{2} C = 2

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In a ΔABC, if sin2A+sin2B+sin2C=2, then the triangle can be

The correct option is B right angledWe can consider triangle ABC as a right triangle. But most appropriately we can say it a right isosceles triangle. As its terms also satisfy the law: sin2A+sin2B+sin2C=2+2cosA.cosB.cosC Thus, 2cosA.cosB.cosC can only be diminished if one of them is right angle.

In a $Δ A B C$ , if ${sin}^{2} A + {sin}^{2} B + {sin}^{2} C = 2$ , then the triangle can be