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{ = }\frac{15}{17} \end{gathered}$$\begin{gathered} \text{ sin }\theta\text{ = }\frac{opposite}{\text{hypotenus}} \\ \text{ Sin }\theta\text{ = }\frac{y}{z} \\ \text{ sin }\theta\text{ = }\frac{8}{17} \end{gathered}$$\begin{gathered} \tan \text{ }\theta\text{ = }\frac{opposite}{\text{adjacent}} \\ \tan \text{ }\theta\text{ = }\frac{y}{x} \\ \tan \text{ }\theta\text{ = }\frac{8}{15} \end{gathered}$$\begin{gathered} \text{ for angle }\phi \\ \text{x = opposite, y = adjacent, and z = hypotenus} \\ \cos \text{ }\phi\text{ = }\frac{adjacent}{\text{hypotenus}} \\ \cos \text{ }\phi\text{ = }\frac{y}{z} \\ \cos \text{ }\phi\text{ = }\frac{8}{17} \end{gathered}$$\begin{gathered} \text{ sin }\phi\text{ = }\frac{opposite}{\text{hypotenus}} \\ \text{ sin }\phi\text{ = }\frac{x}{z} \\ \sin \text{ }\phi\text{ = }\frac{15}{17} \end{gathered}$$\begin{gathered} \tan \text{ }\phi\text{ = }\frac{opposite}{\text{adjacent}} \\ \tan \text{ }\phi\text{ = }\frac{x}{y} \\ \tan \text{ }\phi\text{ = }\frac{15}{8} \end{gathered}$