Question

Give each trig ratio as a fraction in simplest form. PQ is 48.

Answer 1

sin Q = 7/25

cos Q = 24/25

tan Q = 7/24

sin R = 24/25

cos R = 7/25

tan R = 24/7

Step-by-step explanation:
`\begin{gathered} when\text{ Angle = Q} \\ \text{opposite = side opposite the angle= PR} \\ PR\text{ = 14} \\ \text{hypotenuse = 50} \\ \\ \sin \text{ Q = }(opposite)/(hypotenuse) \\ \sin \text{ Q = }(14)/(50) \\ \sin \text{ Q = 7/25} \end{gathered}`
`\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 = }(48)/(50) \\ \cos \text{ Q = 24/25} \end{gathered}`
`\begin{gathered} \tan \text{ Q = }(opposite)/(adjacent) \\ \tan \text{ Q = }(14)/(48) \\ \tan \text{ Q = 7/24} \end{gathered}`

when angle = R

opposite = side opposite the angle R = PQ

opposite = PQ = 48

adjacent = 14

hypotenuse = 50

`\begin{gathered} \sin \text{ R = }(opposite)/(hypotenuse) \\ \sin \text{ R = }(48)/(50) \\ \sin \text{ R = 24/25} \end{gathered}`
`\begin{gathered} \cos \text{ R = }\frac{\text{adjacent}}{\text{hypotenuse}} \\ \text{cos R = }(14)/(50) \\ \cos \text{ R = 7/25} \end{gathered}`
`\begin{gathered} \tan \text{ R = }(opposite)/(hypotenuse) \\ \tan \text{ R = }(48)/(14) \\ \tan \text{ R = 24/7} \end{gathered}`