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

50 degrees
50 degrees

15 degrees
15 degrees

119 degrees
119 degrees

63 degrees
63 degrees

Answer 1

To find the measure of ∠A in triangle ABC using the Law of Cosines, we can apply the following formula:

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

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

Plugging in the values:

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

Calculating the squares:

\[
6^2 = 36, \quad 9^2 = 81, \quad 13^2 = 169
\]

Now substituting these values into the equation:

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

Now we need to find the angle A by taking the arccosine:

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

Calculating this value using a calculator:

\[
A \approx 119^\circ
\]

Thus, the measure of ∠A is approximately **119 degrees**.

The response to choose is:
**119 degrees**.