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

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Weighted averages: word problems

Full solution

Q. In

\triangle \mathrm{NOP}

, the measure of

\angle \mathrm{P}=90^{\circ}, \mathrm{NP}=3, \mathrm{PO}=4

, and

\mathrm{ON}=5

. What is the value of the sine of

\angle \mathrm{N}

to the nearest hundredth?

Identify Triangle and Sides: Question Prompt: Calculate the sine of $\angle N$ in triangle NOP where $\angle P=90^\circ$ , $NP=3$ , $PO=4$ , and $ON=5$ .
Use Sine Definition: Identify the right triangle and the sides. Since $\angle P$ is $90$ degrees, triangle $NOP$ is a right triangle with $NP$ as the opposite side, $PO$ as the adjacent side, and $ON$ as the hypotenuse for angle $N$ .
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, $\sin(N) = \frac{NP}{ON}$ .
Calculate Decimal Value: Plug in the values. $NP = 3$ and $ON = 5$ . Therefore, $\sin(N) = \frac{3}{5}$ .
Round to Nearest Hundredth: Calculate the decimal value. $3$ divided by $5$ equals $0.6$ .
Round to Nearest Hundredth: Calculate the decimal value. $3$ divided by $5$ equals $0.6$ . Round to the nearest hundredth. $0.6$ rounded to the nearest hundredth is $0.60$ .

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