Answer:
[tex]9^{\circ}[/tex]
Step-by-step explanation:
We have been given a right triangle and we re asked to find the measure of angle N to the nearest whole number.
Since measure of all three sides of the triangle is given, so we can use any of the trigonometric ratios to solve our given problem.
[tex]\text{sin}=\frac{\text{Opposite}}{\text{Hypotenuse}}[/tex]
[tex]\text{sin}(N)=\frac{13}{85}[/tex]
Using arcsin we will get,
[tex]N=\text{sin}^{-1}(\frac{13}{85})[/tex]
[tex]N=8.797410709991^{\circ}[/tex]
Upon rounding our answer to nearest whole degree, we will get
[tex]N\approx 9^{\circ}[/tex]
Therefore, the measure of N is 9 degrees.
