Answer:
[tex]\angle P\approx67.38\textdegree[/tex]
Step-by-step explanation:
We want to find the measure of ∠P.
To do so, we can use one of the three trigonometric functions.
Since we know the lengths of all of the sides, it doesn't matter which one we use: we will get the same result.
Let's use the sine ratio. Recall that sine is the ratio of the opposite side to the hypotenuse. That is:
[tex]\displaystyle \sin(x)=\frac{\text{opposite}}{\text{hypotenuse}}[/tex]
Substitute ∠P for x. So:
[tex]\displaystyle \sin(\angle P)=\frac{\text{opposite}}{\text{hypotenuse}}[/tex]
The opposite side to ∠P is 12. The hypotenuse is 13. Hence:
[tex]\displaystyle \sin(\angle P)=\frac{12}{13}[/tex]
We can take the inverse sine of both sides:
[tex]\displaystyle \angle P=\sin^{-1}\left(\frac{12}{13}\right)[/tex]
Use a calculator. Make sure you're in degrees mode!
So, the measure of our angle is:
[tex]\angle P\approx67.38\textdegree[/tex]
And we're done!
