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

15 degrees
15 degrees

50 degrees
50 degrees

119 degrees
119 degrees

63 degrees

Answer 1

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

\[
c^2 = a^2 + b^2 - 2ab \cdot \cos(A)
\]

In this case, we have:

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

We can rearrange the formula to solve for \( \cos(A) \):

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

Now substitute in the values:

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

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

2. Now plug these into the equation:

\[
\cos(A) = \frac{169 + 36 - 81}{2 \cdot 13 \cdot 6}
\]

This simplifies to:

\[
\cos(A) = \frac{124}{156}
\]

3. Simplify \( \frac{124}{156} \):

This reduces to:

\[
\cos(A) = \frac{62}{78} = \frac{31}{39}
\]

4. Now calculate \( A \):

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

\[
A = \cos^{-1}\left(\frac{31}{39}\right)
\]

Using a calculator:

\[
A \approx 63.3^\circ
\]

Thus, the closest measure of \( A \) in the options given is:

**63 degrees**.