Question

In triangle abc , cosa =7/8 ,cosb=11/16 then cos c =

Answer 1

Answer:

Step-by-step explanation:

In a triangle A + B + C = 180 so A + B = 180 - C

cos(A + B) = cos(180 - C) = -cosC

cosAcosB - sinAsinB = -cosC using compound angle identity

If cosA = 7/8 then sinA = √(1 - cos²A) = (√15)/8

Similarly If cosB = 11/16 then sinB = (√135)/16

Therefore cosC = sinAsinB - cosAcosB = [(√15)/8*(√135)/16] - [(7/8)(11/16)]

= [(√2025 - 77)]/(8*16) = (45 - 77)/(8*16) = -32/(8*16) = - ¼

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