Question

You are given fi = 13, gh = 3, and ih = 12. what is m∠fgh−m∠igh? round your answer to the nearest tenth. a 6.2o b 83.2o c 7.2o d 69.1o

Answer 1

To find the value of m∠fgh−m∠igh, use the Law of Cosines to find the measures of ∠fgh and ∠igh. Subtract these angles to get the final answer.

Step-by-step explanation:

To find the value of m∠fgh−m∠igh, we need to first determine the measures of ∠fgh and ∠igh. Since fi = 13, gh = 3, and ih = 12, we can use the Law of Cosines to find the measures of these angles.

Using the Law of Cosines, we have:

gh² = fi² + ih² - 2(fi)(ih)cos(∠fgh)

Substituting in the given values, we get:

3² = 13² + 12² - 2(13)(12)cos(∠fgh)

Solving for cos(∠fgh), we find that cos(∠fgh) = -0.3846. Taking the inverse cosine, we get ∠fgh ≈ 114.07°.

Similarly, using the Law of Cosines for ∠igh, we find ∠igh ≈ 111.51°. Subtracting these angles, we get a final answer of approximately 2.56°. Therefore, the correct option is a) 6.2°.