Question

5664 CRE cas TamahomeAB = 20AC = 16BC = 12

Answer 1

The trigonometric ratios are given by the expressions:

`\begin{gathered} \sin (\theta)=\frac{\text{ Opposite side}}{\text{Hypotenuse}} \\ \cos (\theta)=\frac{\text{ Adjacent side}}{\text{Hypotenuse}} \\ \tan (\theta)=\frac{\text{Opposite side}}{\text{Adjacent side}} \end{gathered}`

Graphically,

So, for angle A you have

`\begin{gathered} \sin (A)=(12)/(20) \\ \sin (A)=(3\cdot4)/(5\cdot4) \\ \sin (A)=(3)/(5) \\ \text{ or} \\ \sin (A)=\text{0}.6 \end{gathered}`
`\begin{gathered} \cos (A)=(16)/(20) \\ \cos (A)=(4\cdot4)/(4\cdot5) \\ \cos (A)=(4)/(5) \\ \text{ or} \\ \cos (A)=0.8 \end{gathered}`
`\begin{gathered} \tan (A)=(12)/(16) \\ \tan (A)=(3\cdot4)/(4\cdot4) \\ \tan (A)=(3)/(4) \\ \text{ or} \\ \tan (A)=0.75 \end{gathered}`

Now, for angle B you have

`\begin{gathered} \sin (B)=(16)/(20) \\ \sin (B)=(4\cdot4)/(5\cdot4) \\ \sin (B)=(4)/(5) \\ \text{ or} \\ \sin (B)=\text{0}.8 \end{gathered}`
`\begin{gathered} \cos (B)=(12)/(20) \\ \cos (B)=(3\cdot4)/(5\cdot4) \\ \cos (B)=(3)/(5) \\ \text{ or} \\ \cos (B)=0.6 \end{gathered}`
`\begin{gathered} \tan (B)=(16)/(12) \\ \tan (B)=(4\cdot4)/(3\cdot4) \\ \tan (B)=(4)/(3) \\ \text{ or} \\ \tan (B)=1.3 \end{gathered}`

Therefore,