Question

In triangle NOP p equals 600 inches angle P equals 96° and angle N equals 64° what is the area of triangle NOP to the nearest 10th of a square inch?

Answer 1

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Answer:

  55,637.8 square inches

Step-by-step explanation:

We can find side n using the Law of Sines:

  n/sin(N) = p/sin(P)

  n = p(sin(N)/sin(P)) = 600·sin(64°)/sin(96°)

  n ≈ 542.246913 . . . . inches

The angle O is ...

  O = 180° -N -P = 180° -64° -96° = 20°

Then the area is ...

  A = 1/2·np·sin(O)

  A = (1/2)(542.246913 in)(600 in)·sin(20°) ≈ 55,637.81008 in²

The area of ∆NOP is about 55,637.8 in².