sin Q = 7/25
cos Q = 24/25
tan Q = 7/24
sin R = 24/25
cos R = 7/25
tan R = 24/7
Explanation:[tex]\begin{gathered} when\text{ Angle = Q} \\ \text{opposite = side opposite the angle= PR} \\ PR\text{ = 14} \\ \text{hypotenuse = 50} \\ \\ \sin \text{ Q = }\frac{opposite}{hypotenuse} \\ \sin \text{ Q = }\frac{14}{50} \\ \sin \text{ Q = 7/25} \end{gathered}[/tex][tex]\begin{gathered} \cos \text{ Q = }\frac{\text{adjacent}}{\text{hypotenuse}} \\ adjacent\text{ = PQ = ?} \\ \text{To get adjacent, we will apply pythagoras' theorem:} \\ \text{hypotenuse}^2=opposite^2+adjacent^2 \\ 50^2=14^2\text{ }+adjacent^2 \\ adjacent^2=50^2-14^2\text{ = 2500 - }196 \\ adjacent^2=\text{ 2304} \\ \text{adjacent = }\sqrt[]{2304}\text{ = 48} \\ \\ \cos \text{ Q = }\frac{48}{50} \\ \cos \text{ Q = 24/25} \end{gathered}[/tex][tex]\begin{gathered} \tan \text{ Q = }\frac{opposite}{adjacent} \\ \tan \text{ Q = }\frac{14}{48} \\ \tan \text{ Q = 7/24} \end{gathered}[/tex]
when angle = R
opposite = side opposite the angle R = PQ
opposite = PQ = 48
adjacent = 14
hypotenuse = 50
[tex]\begin{gathered} \sin \text{ R = }\frac{opposite}{hypotenuse} \\ \sin \text{ R = }\frac{48}{50} \\ \sin \text{ R = 24/25} \end{gathered}[/tex][tex]\begin{gathered} \cos \text{ R = }\frac{\text{adjacent}}{\text{hypotenuse}} \\ \text{cos R = }\frac{14}{50} \\ \cos \text{ R = 7/25} \end{gathered}[/tex][tex]\begin{gathered} \tan \text{ R = }\frac{opposite}{hypotenuse} \\ \tan \text{ R = }\frac{48}{14} \\ \tan \text{ R = 24/7} \end{gathered}[/tex]
