In-ABC-given-a-5-b-7-amp-c-4-If-CAB-then-cot-1-2-

Question Number 144164 by bobhans last updated on 22/Jun/21

In Δ ABC given a = 5, b = 7 & c = 4 .

If ∡ CAB = α then \cot (\frac{1}{2} α) = ?

Answered by liberty last updated on 22/Jun/21

\cot (\frac{1}{2} α) = \sqrt{\frac{s (s - a)}{(s - b) (s - c)}}

where s = \frac{a + b + c}{2} = \frac{5 + 7 + 4}{2} = 8

then \cot (\frac{1}{2} α) = \sqrt{\frac{8 (8 - 5)}{(8 - 7) (8 - 4)}}

= \sqrt{\frac{8.3}{1.4}} = \sqrt{6}

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