Question

If in $\Delta ABC,\angle A={90}^o,a=25cm,b=7cm$ then write all the trigonometric ratios for $\angle B$ and $\angle C$

Answer 1

$△ABC$ is a right-angled triangle where $a$ is the hypotenuse

$b^2+c^2=a^2\Rightarrow c^2=a^2-b^2=625-49=576\Rightarrow c=24cm$

$\cos B=\frac{adjacent}{hypotenuse}=\frac{24}{25}$ and $\sin B=\frac{opposite}{hypotenuse}=\frac{7}{25}$

$\Rightarrow \tan B=\frac{\sin B}{\cos B}=\frac{7}{24}\cot B=\frac{1}{\tan B}=\frac{24}{7}\csc B=\frac{1}{\sin B}=\frac{25}{7}\sec B=\frac{1}{\cos B}=\frac{25}{24}$

Similarly, $\cos C=\frac{adjacent}{hypotenuse}=\frac{7}{25}$ and $\sin C=\frac{opposite}{hypotenuse}=\frac{24}{25}$

$\Rightarrow \tan C=\frac{\sin C}{\cos C}=\frac{24}{7}\cot C=\frac{1}{\tan C}=\frac{7}{24}\csc C=\frac{1}{\sin C}=\frac{25}{24}\sec C=\frac{1}{\cos C}=\frac{25}{7}$