Answer:
12.3 feet.
Step-by-step explanation:
As we are given that [tex]\triangle NOP[/tex] is an right angled triangle.
[tex]\angle P = 90 ^\circ \\\angle N = 59 ^\circ\\Side\ PN = 7.4 \text{ feet}[/tex]
And we have to find out the value of side OP to the nearest tenth of a foot by rounding off the value as seen in the attached figure as well.
By using Trigonometric functions in a right angled [tex]\triangle[/tex], we know that:
[tex]tan \theta = \frac{Perpendicular}{Base}[/tex]
Here, [tex]\theta[/tex] is [tex]\angle N[/tex], Perpendicular is side OP and Base is side PN.
So, [tex]tan 59^\circ = \frac{OP}{PN}[/tex]
[tex]\Rightarrow OP = PN \times tan59^\circ[/tex]
Putting the values of PN and [tex]tan59^\circ[/tex].
[tex]OP = 1.66 \times 7.4\\\Rightarrow OP = 12.3 ft[/tex]
Hence, the value of OP is [tex]12.3\ feet[/tex].
