Question

If in oblique ΔABC side a=13 m, side b=6 m, and side c=9 m, then use the Law of Cosines to find the measure of ∠A.(1 point)Responses63 degrees63 degrees15 degrees15 degrees119 degrees119 degrees50 degrees

Answer 1

To find the measure of angle \( A \) in triangle \( ABC \) using the Law of Cosines, we can use the formula:

\[
\cos A = \frac{b^2 + c^2 - a^2}{2bc}
\]

where:
- \( a = 13 \, m \)
- \( b = 6 \, m \)
- \( c = 9 \, m \)

Now, substituting the values into the formula:

\[
\cos A = \frac{6^2 + 9^2 - 13^2}{2 \cdot 6 \cdot 9}
\]

Calculating each term:

- \( 6^2 = 36 \)
- \( 9^2 = 81 \)
- \( 13^2 = 169 \)

So, we have:

\[
\cos A = \frac{36 + 81 - 169}{2 \cdot 6 \cdot 9}
\]
\[
\cos A = \frac{117 - 169}{108}
\]
\[
\cos A = \frac{-52}{108}
\]
\[
\cos A = -\frac{13}{27}
\]

Now, to find \( A \), we take the inverse cosine:

\[
A = \cos^{-1}\left(-\frac{13}{27}\right)
\]

Calculating \( A \):

Using a calculator:

\[
A \approx 119 \text{ degrees}
\]

Thus, the measure of \( \angle A \) is approximately **119 degrees**.