This is a right triangle.
To find length PQ we need to use the pythagorean theorem; we have to remember that it states that:
[tex]c^2=a^2+b^2[/tex]
where a and b are the legs and c is the hypotenuse.
Applying it to the triangle given we have:
[tex]\begin{gathered} 25^2=PQ^2+24^2 \\ PQ^2=25^2-24^2 \\ PQ^2=625-576 \\ PQ^2=49 \\ PQ=\sqrt[]{49} \\ PQ=7 \end{gathered}[/tex]
Therefore the side PQ=7
To determine the angle R we can use the cosine function that is defined as:
[tex]\cos \theta=\frac{\text{adj}}{\text{ hyp}}[/tex]
then for angle R we have:
[tex]\begin{gathered} \cos R=\frac{24}{25} \\ R=\cos ^{-1}(\frac{24}{25}) \\ R=16.26 \end{gathered}[/tex]
Hence angle R=16.26°.
Now, for angle P we use the fact that the interior angles of any triangle have to add to 180°, then we have:
[tex]\begin{gathered} P+R+Q=180 \\ P+16.26+90=180 \\ P=180-90-16.26 \\ P=73.74 \end{gathered}[/tex]
Therefore angle P=73.74°
