Question

Does someone knows how to do this one?

Answer 1

Answer:

  c) BC/tan(20°)

Step-by-step explanation:

The mnemonic SOH CAH TOA can help you remember the relations between trig functions and angles. It tells you ...

  Sin = Opposite/Hypotenuse

  Cos = Adjacent/Hypotenuse

  Tan = Opposite/Adjacent

In the case of the present triangle, these relations mean ...

  sin(B) = AC/BC   ⇒   AC = BCsin(70°)

  cos(C) = AC/BC   ⇒   AC = BCcos(20°)

  tan(B) = AC/BA   ⇒   AC = BAtan(70°)

  tan(C) = BA/AC   ⇒   AC = BA/tan(20°)

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The answer choice that is not on this list is ...

  c) BC/tan(20°) . . . . . . not equivalent to AC

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Additional comment

The interior angle at C is the supplement of the given angle 160°. These angles form a linear pair.

  C = 180° -160° = 20°

The interior angle at B is the complement of the interior angle at C.

  B = 90° -20° = 70°