Question

In \(△ABC\), if \(a = 13,b = 14,c = 15\), then the value of \(sinA+cosA\) is...

• A. \(\frac{3}{5}\)
• B. \(\frac{7}{5}\)
• C. \(\frac{4}{5}\)
• D. \(\frac{12}{5}\)

Hint:

Find \(\cos A\) by the cosine rule, then \(\sin A\).

Answer 1

The Correct Option is B

Step 1: Use the area
Semi-perimeter $s=21$, area $=\sqrt{21\cdot8\cdot7\cdot6}=84$. Also area $=\tfrac12bc\sin A=105\sin A$.

Step 2: Solve
$\sin A=84/105=4/5$, and $\cos A=3/5$ (A is acute since $a$ is not the longest side). The sum is $7/5$, option (B).

Final Answer:
The sum is $7/5$, option (B). \[ \boxed{\dfrac75} \]