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Question: If in a triangle \(( s - a ) ( s - b ) = s ( s - c )\), then angle C is equal to....

If in a triangle (s−a)(s−b)=s(s−c)( s - a ) ( s - b ) = s ( s - c ), then angle C is equal to.

A

90∘90 ^ { \circ }

B

45∘45 ^ { \circ }

C

30∘30 ^ { \circ }

D

60∘60 ^ { \circ }

Answer

90∘90 ^ { \circ }

Explanation

Solution

tan⁡C2=(s−a)(s−b)s(s−c)=1\tan \frac { C } { 2 } = \sqrt { \frac { ( s - a ) ( s - b ) } { s ( s - c ) } } = 1 =tan⁡(π4)= \tan \left( \frac { \pi } { 4 } \right), from given data.

Hence C=90∘C = 90 ^ { \circ }.