Question

Use the law of cosines, a2 = b2 + c2 -2bc . cos A, to find the value of angle A in a right triangle, where a = 7, b = 24, and c = 25
16.3
73.6
89.9
25.1

Answer 1

In a right triangle, by definition, angle \( C \) (the right angle) equals \( 90^\circ \). Therefore, we can apply the law of cosines to solve for angle \( A \).

Given the values:
- \( a = 7 \)
- \( b = 24 \)
- \( c = 25 \)

The law of cosines states:

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

We need to input our values into the equation:

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

Calculating the squares:

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

Combine the right side:

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

Now, isolate \( \cos A \):

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

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

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

Using a calculator to find \( A \):

\[
A \approx 16.3^\circ
\]

Therefore, the value of angle \( A \) is approximately **16.3 degrees**.