Given:
In ΔPQR, the measure of ∠R=90°, QP = 85, RQ = 13, and PR = 84.
To find:
The cosecant of ∠P.
Solution:
In a right angle triangle,
[tex]\text{cosec}\theta =\dfrac{Hypotenuse}{Perpendicular}[/tex]
It is also written as:
[tex]\text{cosec}\theta =\dfrac{Hypotenuse}{Opposite}[/tex]
In triangle PQR, QP is the hypotenuse because ∠R=90°.
[tex]\text{cosec}P =\dfrac{QP}{RQ}[/tex]
[tex]\text{cosec}P =\dfrac{85}{13}[/tex]
Therefore, the required trigonometric ratio is [tex]\text{cosec}P =\dfrac{85}{13}[/tex].
