Question:
The sides of a triangle \(ABC\) are given by \(a=3\), \(b=5\), and \(c=3\). Then \(\cos A=\)
The sides of a triangle \(ABC\) are given by \(a=3\), \(b=5\), and \(c=3\). Then \(\cos A=\)
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When three sides of a triangle are given and an angle has to be found, use the cosine rule:
\[
\cos A=\frac{b^2+c^2-a^2}{2bc}
\]
Updated On: Jun 26, 2026
- \(\dfrac{2}{6}\)
- \(\dfrac{1}{6}\)
- \(\dfrac{2}{3}\)
- \(\dfrac{5}{6}\)
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The Correct Option is D
Solution and Explanation
Step 1: Use cosine rule.
In a triangle, \[ a^2=b^2+c^2-2bc\cos A \] Therefore, \[ \cos A=\frac{b^2+c^2-a^2}{2bc} \]
Step 2: Substitute the given values.
Given, \[ a=3,\quad b=5,\quad c=3 \] So, \[ \cos A=\frac{5^2+3^2-3^2}{2(5)(3)} \]
Step 3: Simplify.
\[ \cos A=\frac{25+9-9}{30} \] \[ \cos A=\frac{25}{30} \] \[ \cos A=\frac{5}{6} \]
Step 4: Final conclusion.
Therefore, \[ \boxed{\frac{5}{6}} \]
In a triangle, \[ a^2=b^2+c^2-2bc\cos A \] Therefore, \[ \cos A=\frac{b^2+c^2-a^2}{2bc} \]
Step 2: Substitute the given values.
Given, \[ a=3,\quad b=5,\quad c=3 \] So, \[ \cos A=\frac{5^2+3^2-3^2}{2(5)(3)} \]
Step 3: Simplify.
\[ \cos A=\frac{25+9-9}{30} \] \[ \cos A=\frac{25}{30} \] \[ \cos A=\frac{5}{6} \]
Step 4: Final conclusion.
Therefore, \[ \boxed{\frac{5}{6}} \]
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