The sides of a triangle are respectively 7 cm - 4 -3 cm and -1 3 cm- then the smallest angle of the triangle isA- - - 4B- - - 5C- - - 3D- - - 6

The correct option is D π/6 Let a = 7 cm, b = 4√(3) and c=√(1)3 cm. Here, we see that the smallest side is c. Therefore, the smallest angle will be C. ∴ cosC=a ...

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Standard XII

Physics

Multiplication & Division of Errors

The sides of ...

Question

The sides of a triangle are respectively 7 cm, $4 \sqrt{3}$ cm and $\sqrt{1} 3$ cm, then the smallest angle of the triangle is

π/6

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π/3

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π/4

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π/5

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Solution

The correct option is A
π/6

Let a = 7 cm, b = $4 \sqrt{3}$ and c= $\sqrt{1} 3$ cm. Here, we see that the smallest side is c. Therefore, the smallest angle will be C.

$∴ c o s C = \frac{a^{2} + b^{2} - c^{2}}{2 a b} = \frac{(7)^{2} + (4 \sqrt{3})^{2} - (\sqrt{1} 3)^{2}}{2 \times 7 \times 4 \sqrt{3}} = \frac{49 + 48 - 13}{56 \sqrt{3}} = \frac{\sqrt{3}}{2} \Rightarrow C = \frac{π}{6}$

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The sides of a triangle are respectively 7 cm, 4√3cm and √13cm, then the smallest angle of the triangle is

The correct option is A π/6 Let a = 7 cm, b = 4√3 and c=√13 cm. Here, we see that the smallest side is c. Therefore, the smallest angle will be C. ∴cosC=a2+b2−c22ab=(7)2+(4√3)2−(√13)22×7×4√3=49+48−1356√3=√32⇒C=π6

The sides of a triangle are respectively 7 cm, $4 \sqrt{3}$ cm and $\sqrt{1} 3$ cm, then the smallest angle of the triangle is