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Area of a Triangle

In a right an...

Question

In a right angle triangle $△ A B C, {sin}^{2} A + {sin}^{2} B + {sin}^{2} C$ is

0

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None of these

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Solution

The correct option is D None of these
Let $C = 90^{0}$
Then,
${sin}^{2} A + {sin}^{2} B + {sin}^{2} C = {sin}^{2} A + {sin}^{2} B + 1$
$= {sin}^{2} A + {sin}^{2} (\frac{π}{2} - A) + 1 = {sin}^{2} A + {cos}^{2} A + 1 = 1 + 1 = 2$

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Similar questions

A

B

C

∣ ∣ ∣ ∣ ∣ \begin{matrix} 1 & 1 & 1 1 + sin A & 1 + sin B & 1 + sin C sin A + {sin}^{2} A & sin B + {sin}^{2} B & sin C + {sin}^{2} C \end{matrix} ∣ ∣ ∣ ∣ ∣ = 0

Δ

A + B + C = 180^{o}

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

{sin}^{2} A + {sin}^{2} B + {sin}^{2} C = 2 (1 + cos A cos B cos C)

a, b, c

H . P .

{sin}^{2} \frac{1}{2} A, {sin}^{2} \frac{1}{2} B, {sin}^{2} \frac{1}{2} C

H . P .

A B C

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

A, B

C

∣ ∣ ∣ ∣ ∣ \begin{matrix} 1 & 1 & 1 1 + sin A & 1 + sin B & 1 + sin C sin A + {sin}^{2} A & sin B + {sin}^{2} B & sin C + {sin}^{2} C \end{matrix} ∣ ∣ ∣ ∣ ∣ = 0

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