Question

Help please! these questions are really confusing me

Answer 1

Answer:

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:  $\frac{\textbf{4}}{\textbf{5}}$  ;  $\frac{\textbf{3}}{\textbf{5}}$ ;  $\frac{\textbf{4}}{\textbf{3}}$

Step-by-step 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 = $\frac{6\sqrt{3}}{12}$  = $\frac{\sqrt{3}}{2}$

Cos A = $\frac{6}{12} = \frac{1}{2}$

Tan A = $\frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}}$  = $\sqrt{3}$

Figure 2:

Sin A = $\frac{2\sqrt{19}}{20}$  = $\frac{\sqrt{19}}{10}$

Cos A = $\frac{18}{20} = \frac{9}{10}$

Tan A = $\frac{\frac{\sqrt{19}}{10}}{\frac{10}{9}}$ = $\frac{\sqrt{19}}{9}$

Figure 3:

Sin A =   $\frac{16}{20}$   = $\frac{4}{5}$

Cos A = $\frac{12}{20} = \frac{3}{5}$

Tan A = $\frac{\frac{4}{5}}{\frac{3}{5}}$  = $\frac{4}{3}$

Hence, the answer.