Question

Use the Law of Cosines,
B2 = a2 +C2 - 2ac-cos B, to find the
value of angle
B in a right triangle, where
a = 9,
b = 40, and
c =41. (1 point)
• 90.01 degrees
• 77.32 degrees
• 78.01 degrees
• 84.55 degrees

Answer 1

To find angle \( B \) in a triangle using the Law of Cosines, we can rearrange the formula as follows:

\[
\cos B = \frac{a^2 + c^2 - b^2}{2ac}
\]

Given:
- \( a = 9 \)
- \( b = 40 \)
- \( c = 41 \)

Now, we need to calculate \( a^2 \), \( c^2 \), and \( b^2 \):

\[
a^2 = 9^2 = 81
\]
\[
b^2 = 40^2 = 1600
\]
\[
c^2 = 41^2 = 1681
\]

Next, substitute these values into the rearranged Law of Cosines formula:

\[
\cos B = \frac{81 + 1681 - 1600}{2 \times 9 \times 41}
\]

Now calculate the numerator:

\[
81 + 1681 - 1600 = 162
\]

Now calculate the denominator:

\[
2 \times 9 \times 41 = 738
\]

Now we can find \( \cos B \):

\[
\cos B = \frac{162}{738}
\]

Calculating that gives:

\[
\cos B \approx 0.219
\]

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

\[
B = \cos^{-1}(0.219) \approx 77.32 \text{ degrees}
\]

Thus, the value of angle \( B \) is approximately:

**77.32 degrees**

So the correct answer is:

• 77.32 degrees