Given:
In ΔPQR, the measure of ∠R=90°, the measure of ∠P=52°, and QR = 9.6 feet.
We need to determine the length of RP.
Length of RP:
The image of the triangle PQR is attached below.
Using the figure, the length of RP can be determined using the trigonometric ratio,
[tex]tan \ \theta=\frac{opp}{adj}[/tex]
Substituting [tex]\theta=52^{\circ}[/tex], [tex]opp=QR[/tex] and [tex]adj=RP[/tex]
Thus, we get;
[tex]tan \ 52^{\circ}=\frac{QR}{RP}[/tex]
Substituting the values, we get;
[tex]1.2799=\frac{9.6}{RP}[/tex]
Simplifying, we get;
[tex]RP=\frac{9.6}{1.2799}[/tex]
Dividing, we get;
[tex]RP=7.5[/tex]
Thus, the length of RP is 7.5 feet.
