Question

In $△ABC$, right angled at $B$, $AB=24cm,BC=7cm$. Determine$:\left(i\right)\sin A,\cos A,\left(ii\right)\sin C,\cos C$

• A. $\sin A=\cos C=\frac{5}{21}$, $\cos A=\sin C=\frac{21}{25}$,
  
• B. $\sin A=\cos C=\frac{11}{24}$, $\cos A=\sin C=\frac{17}{25}$,
• C. $\sin A=\cos C=\frac{7}{25}$, $\cos A=\sin C=\frac{24}{25}$,
• D. None of these
  

Answer 1

Answer: (C)

$\sin A=\cos C=\frac{7}{25}$, $\cos A=\sin C=\frac{24}{25}$,

By Pythagoras Theorem,
$A{C}^2=A{B}^2+B{C}^2=(24{)}^2+(7{)}^2=625$
$\Rightarrow AC=\sqrt{625}=25cm$
$\left(i\right)\sin A=\frac{BC}{AC}\{i.e.,\frac{\text{side opposite to angle A}}{Hyp.}\}$
$=\frac{7}{25}(\because BC=7cm\text{and}AC=25cm)$
$\cos A=\frac{AB}{AC}\{i.e.,\frac{\text{side adjacent to angle A}}{Hyp.}\}$
$=\frac{24}{25}(\because AB=24cm\text{, and}AC=25cm)$
$\left(ii\right)\sin C=\frac{AB}{AC}\{i.e.,\frac{\text{side opposite to angle C}}{Hyp.}\}=\frac{24}{25}$
$\cos C=\frac{BC}{AC}\{i.e.,\frac{\text{side adjacent to angle C}}{Hyp.}\}=\frac{7}{25}$