Question

Suppose x = 15, y = 8 and z = 17. Find the following and enter exact answers as fractions and not decimal approximations

Answer 1

Given that

x = 15

y = 8

z = 17

The various angles can be calculated using SOH CAH TOA RULE

`\begin{gathered} \text{Cos }\theta\text{ = }\frac{Adjacent}{\text{Hypotenus}} \\ \text{x = adjacent, y = opposite and z = hypotenus} \\ \cos \text{ }\theta\text{ = }(15)/(17) \end{gathered}`
`\begin{gathered} \text{ sin }\theta\text{ = }\frac{opposite}{\text{hypotenus}} \\ \text{ Sin }\theta\text{ = }(y)/(z) \\ \text{ sin }\theta\text{ = }(8)/(17) \end{gathered}`
`\begin{gathered} \tan \text{ }\theta\text{ = }\frac{opposite}{\text{adjacent}} \\ \tan \text{ }\theta\text{ = }(y)/(x) \\ \tan \text{ }\theta\text{ = }(8)/(15) \end{gathered}`
`\begin{gathered} \text{ for angle }\phi \\ \text{x = opposite, y = adjacent, and z = hypotenus} \\ \cos \text{ }\phi\text{ = }\frac{adjacent}{\text{hypotenus}} \\ \cos \text{ }\phi\text{ = }(y)/(z) \\ \cos \text{ }\phi\text{ = }(8)/(17) \end{gathered}`
`\begin{gathered} \text{ sin }\phi\text{ = }\frac{opposite}{\text{hypotenus}} \\ \text{ sin }\phi\text{ = }(x)/(z) \\ \sin \text{ }\phi\text{ = }(15)/(17) \end{gathered}`
`\begin{gathered} \tan \text{ }\phi\text{ = }\frac{opposite}{\text{adjacent}} \\ \tan \text{ }\phi\text{ = }(x)/(y) \\ \tan \text{ }\phi\text{ = }(15)/(8) \end{gathered}`