Question

If a=3 b=4 c=5 in a triangle then R=?

Answer 1

Answer:

the question is wrong fully wrong

Answer 2

Answer:

The circumradius of the triangle with given sides is R=2.5 Units

Step-by-step explanation:

Given that,

The values of lengths of sides of a triangle are

$a=3,b=4,c=5$

And we are required to find the value of its circumradius(R).

To find the circumradius,we shall use the Sine rule from the properties of triangle which is written below.

For any $\triangle ABC$,

$\frac{a}{SinA} =\frac{b}{SinB} =\frac{c}{SinC} =2R$

We need to find the value of angle A,which can be found from cosine rule as shown below

$CosA=\frac{b^{2}+c^{2}-a^{2}}{2bc}$

Substituting the given values,we get

$CosA=\frac{4^{2}+5^{2}-3^{2}}{2(4)(5)} =\frac{4}{5} \\= > SinA=\sqrt{1-(\frac{4}{5})^{2} } =\frac{3}{5}$

Substituting the value of SinA in the Sine rule equation,we get

$\frac{a}{SinA} =2R= > \frac{3}{\frac{3}{5} } =2R\\= > R=\frac{5}{2}=2.5units$

Therefore,the circumradius of the triangle with given sides is R=2.5 Units.

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