Question

Use the Law of Cosines,
a2 =B2 + 2 - 2bc •cos A, to find the value of angle
A in a right triangle, where
a = 7,
6 = 24, and
c = 25. (1 point)
• 89.9 degrees
• 16.3 degrees
• 25.1 degrees
• 73.6 degrees

Answer 1

To find the angle \( A \) in the given right triangle using the Law of Cosines, we first need to accurately apply the formula:

\[
a^2 = b^2 + c^2 - 2bc \cdot \cos A
\]

However, in a right triangle, we can also use the relationship:

\[
a^2 + b^2 = c^2
\]

But the Law of Cosines can still be used in general cases. In this case, we assign:

- \( a = 7 \)
- \( b = 24 \)
- \( c = 25 \)

Plugging the values into the Law of Cosines formula:

\[
7^2 = 24^2 + 25^2 - 2 \cdot 24 \cdot 25 \cdot \cos A
\]

Calculating each term:

\[
49 = 576 + 625 - 1200 \cos A
\]

Combining terms on the right side:

\[
49 = 1201 - 1200 \cos A
\]

Rearranging to solve for \( \cos A \):

\[
1200 \cos A = 1201 - 49
\]
\[
1200 \cos A = 1152
\]
\[
\cos A = \frac{1152}{1200}
\]
\[
\cos A = 0.96
\]

Now, we can find \( A \):

\[
A = \cos^{-1}(0.96)
\]

Using a calculator to find the angle:

\[
A \approx 16.26
\]

Thus, rounding to one decimal place:

- \( A \approx 16.3 \) degrees.

The correct answer is:

**16.3 degrees**.