AP EAMCET201921 Apr 2019Evening ShiftMathematicsProperties of TrianglesActual
In Δ A B C , if a : b : c = 3 : 5 : 7 , then cos A + cos B =
Options
- A13 7
- B11 7
- C12 7
- D10 7
Correct answer
C. 12 7
Step-by-step solution
The ratio is given as, a : b : c = 3 : 5 : 7 . Consider a = 3 x ,   b = 5 x ,   c = 7 x . Now, cos A + cos B = b 2 + c 2 - a 2 2 b c + a 2 + c 2 - b 2 2 a c = ( 5 x ) 2 + ( 7 x ) 2 - ( 3 x ) 2 2 ( 5 x ) ( 7 x ) + ( 3 x ) 2 + ( 7 x ) 2 - ( 5 x ) 2 2 ( 3 x ) ( 7 x ) = 65 x 2 70 x 2 + 33 x 2 42 x 2 = 65 70 + 33 42 = 12 7