The measure of side length PM in the right triangle is approximately 16.2 units.
The figure in the image is a right triangle.
From the figure:
Angle N = 34 degrees
Adjacent to angle N = NP = 24 units
Opposite to angle N = PM =?
To solve for the length of side PM, we use the trigonometric ratio:
Note that;
tan ( θ ) = opposite / adjacent
Hence;
tan ( N ) = PM / NP
Plug in the values and solve for PM:
tan ( 34 ) = PM / 24
PM = 24 × tan ( 34 )
PM = 16.188
PM ≈ 16.2 units
Therefore, the side length PM measures approximately 16.2 units.