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

50 degrees
50 degrees

15 degrees

Answer 1

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

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

Given the sides:
- \( a = 13 \, \text{m} \)
- \( b = 6 \, \text{m} \)
- \( c = 9 \, \text{m} \)

We will substitute these values into the formula:

1. Calculate \( b^2 \), \( c^2 \), and \( a^2 \):

\[
b^2 = 6^2 = 36
\]
\[
c^2 = 9^2 = 81
\]
\[
a^2 = 13^2 = 169
\]

2. Substitute these values into the Law of Cosines equation:

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

3. Calculate the numerator:

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

4. Calculate the denominator:

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

5. Now substitute back into the equation:

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

6. Simplify:

\[
\cos A \approx -0.4815
\]

7. Use the inverse cosine function to find angle \( A \):

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

Calculating \( A \) gives:

\[
A \approx 118.93^\circ
\]

Rounding gives:

\[
A \approx 119^\circ
\]

The measure of angle \( A \) is approximately \( 119 \) degrees.

Thus, the correct response is:

**119 degrees**