In - ABC if a-13- b-14- c-15- then tan B-2-

The correct option is C 4/7 In Δ ABC if a=13, b=14, c=15 Then, tanB2=Δs(s b) = √(s(s a)(s b)(s c))s(s b) = #160; #160; √((s ...

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Standard XII

Mathematics

Area between Two Curves

In Δ ABC if...

Question

In $Δ A B C$ if $a = 13, b = 14, c = 15$ , then tan $\frac{B}{2} =$

\frac{3}{7}

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\frac{16}{49}

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\frac{4}{7}

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\frac{2}{\sqrt{7}}

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Solution

The correct option is C $\frac{4}{7}$
In $Δ A B C$ if $a = 13, b = 14, c = 15$
Then, $tan \frac{B}{2} = \frac{Δ}{s (s - b)}$
$= \frac{\sqrt{s (s - a) (s - b) (s - c)}}{s (s - b)}$
$= \sqrt{\frac{(s - c) (s - a)}{s (s - b)}}$
$= \sqrt{\frac{(a + b - c) (b + c - a)}{(a + b + c) (a + c - b)}}$
$= \sqrt{\frac{(13 + 14 - 15) (14 + 15 - 13)}{(13 + 14 + 15) (13 + 15 - 14)}}$
$= \sqrt{\frac{12 \times 16}{42 \times 14}}$
$= \frac{4}{7}$

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In ΔABC if a=13, b=14, c=15, then tan B2=

The correct option is C 47In ΔABC if a=13, b=14, c=15Then, tanB2=Δs(s−b)=√s(s−a)(s−b)(s−c)s(s−b)=√(s−c)(s−a)s(s−b)=√(a+b−c)(b+c−a)(a+b+c)(a+c−b)=√(13+14−15)(14+15−13)(13+14+15)(13+15−14)=√12×1642×14=47

In $Δ A B C$ if $a = 13, b = 14, c = 15$ , then tan $\frac{B}{2} =$