Can we construct a -ABC in which -A -95 - and AB - 5 cm and -C -105 - -

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Standard VIII

Mathematics

The Centroid

Can we constr...

Question

Can we construct a $Δ$ ABC in which $∠$ A $= 95^{\circ}$ , and AB $= 5 c m$ and $∠$ C $= 105^{\circ}$ ?

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Solution

It is not possible to construct a triangle with the given dimensions because sum of it's two angles is more than $180^{\circ}$ $(105^{\circ} + 95^{\circ})$ .
For any triangle to exist, the sum of the three angles must be equal to $180^{\circ}$ .

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Construct a $Δ A B C$ in which AB = 6 cm, $∠ A = 30^{\circ} a n d ∠ B = 60^{\circ} .$ Construct another $Δ A B^{'} C^{'} similar to Δ A B C$ with base AB' = 8 cm.

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Can we construct a ΔABC in which ∠A =95∘, and AB =5cm and ∠C =105∘ ?

It is not possible to construct a triangle with the given dimensions because sum of it's two angles is more than 180∘ (105∘+95∘). For any triangle to exist, the sum of the three angles must be equal to 180∘.

Can we construct a $Δ$ ABC in which $∠$ A $= 95^{\circ}$ , and AB $= 5 c m$ and $∠$ C $= 105^{\circ}$ ?

It is not possible to construct a triangle with the given dimensions because sum of it's two angles is more than $180^{\circ}$ $(105^{\circ} + 95^{\circ})$ .
For any triangle to exist, the sum of the three angles must be equal to $180^{\circ}$ .