Question

If in oblique
ДАВС side
a = 13 m, side
6 = 6 m, and side
c = 9 m, then use the Law of Cosines to
find the measure of
LA. (1 point)
• 50 degrees
• 119 degrees
• 15 degrees
• 63 degrees

Answer 1

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

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

In your case, let's assign the sides as follows:
- \( a = 13 \, m \) (opposite angle \( A \))
- \( b = 6 \, m \) (one side adjacent to angle \( A \))
- \( c = 9 \, m \) (the other side adjacent to angle \( A \))

Now, plug in the values into the formula:

\[
\cos(A) = \frac{b^2 + c^2 - a^2}{2bc} = \frac{6^2 + 9^2 - 13^2}{2 \cdot 6 \cdot 9}
\]

Calculating each term:

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

Now substitute these values back into the equation:

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

Simplifying the fraction:

\[
\cos(A) = \frac{-26}{54} = -\frac{13}{27}
\]

Now, we need to find the angle \( A \):

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

Calculating the value:

Using a calculator to find the inverse cosine, you obtain:

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

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