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If Two Sides of a Triangle Are Unequal, Then the Angle Opposite to the Greater Side Is Greater Than Angle Opposite to the Smaller Side

In Δ PQR, ∠...

Question

In $Δ P Q R, ∠ P Q R = 90^{o}$
seg $Q S ⊥$ hypotenuse $P R$ , if $P S = 4$
$S R = 9$ find $Q S$

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Solution

We have using Pythagorus theorem,
$Q S^{2} = P S . S R$ ......(1) [ Can be proved by applying Pythagorus theorem on the triangles $Δ P Q R$ , $Δ P Q S$ , $Δ Q S R$ ]
Given $P S = 4, S R = 9$ .
Then form (1) we have
$Q S^{2} = 4 \times 9$
or, $Q S^{2} = 36$
or, $Q S = 6$ ,

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If Two Sides of a Triangle Are Unequal, Then the Angle Opposite to the Greater Side Is Greater Than Angle Opposite to the Smaller Side

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