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In /_\NOP, the measure of /_P=90^(@),NP=3,PO=4, and ON=5. What is the value of the sine of /_N to the nearest hundredth?

In △NOP \triangle \mathrm{NOP} , the measure of ∠P=90∘,NP=3,PO=4 \angle \mathrm{P}=90^{\circ}, \mathrm{NP}=3, \mathrm{PO}=4 , and ON=5 \mathrm{ON}=5 . What is the value of the sine of ∠N \angle \mathrm{N} to the nearest hundredth?

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Q. In △NOP \triangle \mathrm{NOP} , the measure of ∠P=90∘,NP=3,PO=4 \angle \mathrm{P}=90^{\circ}, \mathrm{NP}=3, \mathrm{PO}=4 , and ON=5 \mathrm{ON}=5 . What is the value of the sine of ∠N \angle \mathrm{N} to the nearest hundredth?
  1. Identify Triangle and Sides: Question Prompt: Calculate the sine of ∠N\angle N in triangle NOP where ∠P=90∘\angle P=90^\circ, NP=3NP=3, PO=4PO=4, and ON=5ON=5.
  2. Use Sine Definition: Identify the right triangle and the sides. Since ∠P\angle P is 9090 degrees, triangle NOPNOP is a right triangle with NPNP as the opposite side, POPO as the adjacent side, and ONON as the hypotenuse for angle NN.
  3. Plug in Values: Use the sine definition. Sine of an angle in a right triangle is the ratio of the length of the opposite side to the hypotenuse. So, sin⁡(N)=NPON\sin(N) = \frac{NP}{ON}.
  4. Calculate Decimal Value: Plug in the values. NP=3NP = 3 and ON=5ON = 5. Therefore, sin⁡(N)=35\sin(N) = \frac{3}{5}.
  5. Round to Nearest Hundredth: Calculate the decimal value. 33 divided by 55 equals 0.60.6.
  6. Round to Nearest Hundredth: Calculate the decimal value. 33 divided by 55 equals 0.60.6. Round to the nearest hundredth. 0.60.6 rounded to the nearest hundredth is 0.600.60.

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