Question

If $\tan A=\frac{5}{12}$, find the value of $\sin A+\cos A$, where $A$ is an acute angle.

• A. $\frac{13}{17}$
• B. $\frac{17}{13}$
• C. $\frac{12}{5}$
• D. $\frac{5}{17}$

Answer 1

Answer: (B)

$\frac{17}{13}$

Given, $\tan A=\frac{5}{12}$ $=\frac{BC}{AB}$

$\therefore AC=A{B}^2+B{C}^2$

$\Rightarrow A{C}^2=5^2+(12{)}^2$

$\Rightarrow A{C}^2=25+144$

$\Rightarrow A{C}^2=169$

$\Rightarrow AC=13$

Now, $\sin A=\frac{BC}{AC}=\frac{5}{13}$

$\cos A=\frac{AB}{AC}=\frac{12}{13}$

$\therefore \sin A+\cos A$

$=\frac{5}{13}+\frac{12}{13}$

$=\frac{5+12}{13}$

$=\frac{17}{13}$