From the attached picture we can see
The right triangle NPR
NP and PR are its legs
NR is the hypotenuse
x and y are the measures of the 2 acute angles
To find x, we can use the sine ratio
[tex]sin\angle R=\frac{opposite}{hypotenuse}[/tex]
The opposite side is NP = 60
The hypotenuse is NR = 87
Substitute them in the ratio
[tex]sin\angle R=\frac{60}{87}[/tex]
Use the inverse of the sine
[tex]\begin{gathered} \angle R=sin^{-1}(\frac{60}{87}) \\ \angle R=43.60281897^{\circ} \end{gathered}[/tex]
Round it to the nearest whole number, then
[tex]\angle R=44^{\circ}[/tex]
Since x is the measure of angle R, then
x = 44
Since the sum of the measures of the angle of a triangle is 180 degrees, then
[tex]x^{\circ}+y^{\circ}+90^{\circ}=180^{\circ}[/tex]
Substitute x by 44
[tex]\begin{gathered} 44+y+90=190 \\ (44+90)+y=180 \\ 134+y=180 \end{gathered}[/tex]
Subtract 134 from both sides
[tex]\begin{gathered} 134-134+y=180-134 \\ y=46 \end{gathered}[/tex]
The answers are:
x = 44
y = 46
