Question:
In \(△ABC\), if \(a = 13,b = 14,c = 15\), then the value of \(sinA+cosA\) is...
In \(△ABC\), if \(a = 13,b = 14,c = 15\), then the value of \(sinA+cosA\) is...
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Find \(\cos A\) by the cosine rule, then \(\sin A\).
Updated On: Oct 1, 2026
- \(\frac{3}{5}\)
- \(\frac{7}{5}\)
- \(\frac{4}{5}\)
- \(\frac{12}{5}\)
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The Correct Option is B
Solution and Explanation
Step 1: Understanding the Concept
With three sides known, the cosine rule gives the angle \(A\) opposite to \(a\).
Step 2: Key Formula or Approach
\[ \cos A=\frac{b^2+c^2-a^2}{2bc} \]
Step 3: Detailed Explanation
\[ \cos A=\frac{196+225-169}{2\times14\times15}=\frac{252}{420}=\frac35 \]
Then \(\sin A=\sqrt{1-\tfrac{9}{25}}=\tfrac45\).
\[ \sin A+\cos A=\frac45+\frac35=\frac75 \]
Final Answer:
The value is \(7/5\), option (B). \[ \boxed{\dfrac75\ \text{(B)}} \]
With three sides known, the cosine rule gives the angle \(A\) opposite to \(a\).
Step 2: Key Formula or Approach
\[ \cos A=\frac{b^2+c^2-a^2}{2bc} \]
Step 3: Detailed Explanation
\[ \cos A=\frac{196+225-169}{2\times14\times15}=\frac{252}{420}=\frac35 \]
Then \(\sin A=\sqrt{1-\tfrac{9}{25}}=\tfrac45\).
\[ \sin A+\cos A=\frac45+\frac35=\frac75 \]
Final Answer:
The value is \(7/5\), option (B). \[ \boxed{\dfrac75\ \text{(B)}} \]
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