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)
Responses

63 degrees
63 degrees

119 degrees
119 degrees

15 degrees
15 degrees

50 degrees
50 degrees

Answer 1

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

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

Given:

- Side \( a = 13 \) m
- Side \( b = 6 \) m
- Side \( c = 9 \) m

We will substitute these values into the formula.

Calculating \( b^2 \), \( c^2 \), and \( a^2 \):

\[
b^2 = 6^2 = 36
\]

\[
c^2 = 9^2 = 81
\]

\[
a^2 = 13^2 = 169
\]

Now we substitute these values into the cosine formula:

\[
\cos A = \frac{36 + 81 - 169}{2 \cdot 6 \cdot 9}
\]

Calculating the numerator:

\[
36 + 81 - 169 = 117 - 169 = -52
\]

Calculating the denominator:

\[
2 \cdot 6 \cdot 9 = 108
\]

Now substituting back into the cosine equation:

\[
\cos A = \frac{-52}{108}
\]

Calculating this gives:

\[
\cos A = -\frac{52}{108} \approx -0.4815
\]

Now, we need to find \( A \) by taking the inverse cosine:

\[
A = \cos^{-1}(-0.4815)
\]

Using a calculator:

\[
A \approx 118.93^\circ
\]

Rounding to the nearest whole number gives \( A \approx 119^\circ \).

Therefore, the measure of \( \angle A \) is approximately:

**119 degrees**.