Question

Analyze the diagram below and answer the question that follows

Answer 1

Answer:

C. 40.2°

Step-by-step explanation:

Cosine rule (real handy to remember): c² = a² + b² - 2·a·b·cos(γ)

If you don't know this yet, look it up but in short: c, a and b are the lengths of the sides of the triangle, the angle opposite side a is called α, for b it is β and for c it is γ. That's the convention I've always used anyway, you can call them whatever of course. Anyhow:

c² = a² + b² - 2·a·b·cos(γ)

⇒ |AC|² = |AB|²+|BC|²-2·|AB|·|BC|·cos(∠B)

⇒ |AC|²-|AB|²-|BC|² = -2·|AB|·|BC|·cos(∠B)

⇒ ( |AC|²-|AB|²-|BC|² ) / ( -2·|AB|·|BC| ) = cos(∠B)

⇒ ∠B = arccos( ( |AC|²-|AB|²-|BC|² ) / ( -2·|AB|·|BC| ) )

         = arccos( ( 11²-16²-16² ) / ( -2·16·16 ) )

         = 40.21101958°

         ≈ 40.2°