Question

Help please! these questions are really confusing me

Answer 1

Figure 1: Option A :
`$ \sqrt{\frac{\textbf{3}}{\textbf{2}}} $` ;
`$ \frac{\textbf{1}}{\textbf{2}} $` ;
`$ \sqrt{\textbf{3}}} $`

Figure 2: Option B:
`$ \frac{\sqrt{\textbf{19}}}{\textbf{10}} $` ;
`$ \frac{\textbf{9}}{\textbf{10}} $` ;
`$ \frac{\sqrt{\textbf{19}}}{\textbf{9}} $`

Figure 3: Option C:
`$ \frac{\textbf{4}}{\textbf{5}} $` ;
`$ \frac{\textbf{3}}{\textbf{5}} $` ;
`$ \frac{\textbf{4}}{\textbf{3}} $`

Explanation:

`$ \textbf{Sin A} \hspace{1mm} \textbf{= } \hspace{1mm} \frac{\textbf{opp}}{\textbf{hyp}} $`

`$ \textbf{Cos A} \hspace{1mm} {\textbf{=} \hspace{1mm} \frac{\textbf{adj}}{\textbf{hyp}} $`

`$ \textbf{Tan A} \hspace{1mm} \textbf{=} \hspace{1mm} \frac{\textbf{Sin A}}{\textbf{Cos A}} $`

We can simply follow these three formulas to solve the problem.

Figure 1:

Sin A =
`$ (6√(3))/(12) $` =
`$ (√(3))/(2) $`

Cos A =
`$ (6)/(12) = (1)/(2) $`

Tan A =
`$ ((√(3))/(2))/((1)/(2))} $` =
`$ √(3) $`

Figure 2:

Sin A =
`$ (2√(19))/(20) $` =
`$ (√(19))/(10) $`

Cos A =
`$ (18)/(20) = (9)/(10) $`

Tan A =
`$ ((√(19))/(10))/((10)/(9)) $` =
`$ (√(19))/(9) $`

Figure 3:

Sin A =
`$ (16)/(20) $` =
`$ (4)/(5) $`

Cos A =
`$ (12)/(20) = (3)/(5) $`

Tan A =
`$ ((4)/(5))/((3)/(5)) $` =
`$ (4)/(3) $`

Hence, the answer.