Questions: a=5, b=8, c=9, find m angle A

Transcript text: $a=5, b=8, c=9$, find $m \angle A$

Solution

Solution Steps

Step 1: Given Values

Let $ a = 5 $, $ b = 8 $, and $ c = 9 $.

Step 2: Apply the Law of Cosines

Using the Law of Cosines, we calculate $ \cos(A) $ as follows: \[ \cos(A) = \frac{b^2 + c^2 - a^2}{2bc} \] Substituting the values: \[ \cos(A) = \frac{8^2 + 9^2 - 5^2}{2 \cdot 8 \cdot 9} \]

Step 3: Calculate $ \cos(A) $

Calculating the squares: \[ \cos(A) = \frac{64 + 81 - 25}{144} = \frac{120}{144} = \frac{5}{6} \]

Step 4: Find Angle $ A $

To find $ A $, we take the inverse cosine: \[ A = \cos^{-1}\left(\frac{5}{6}\right) \]

Step 5: Convert to Degrees

Finally, convert $ A $ from radians to degrees: \[ A \approx 33.56^\circ \]

Final Answer

$\boxed{33.56^\circ}$

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