**Trigonometry Problem: Using the Law of Cosines to Find an Angle**In the given triangle \( \Delta RST \), the side lengths are as follows: \( r = 3.9 \) inches, \( s = 5.6 \) inches, and \( t = 6.1 \) inches.To find the measure of angle \( \angle S \) to the nearest 10th degree, you can use the Law of Cosines formula:\[ c^2 = a^2 + b^2 - 2ab \cdot \cos(C) \]Where \( a \), \( b \), and \( c \) are the sides of the triangle, and \( C \) is the angle opposite side \( c \).**Step-by-Step Solution:**1. Identify the sides opposite to the angles: - In this case, let side \( r \) be opposite angle \( \angle R \), - side \( s \) be opposite angle \( \angle S \), - and side \( t \) be opposite angle \( \angle T \).2. Rewrite the Law of Cosines for finding \( \angle S \): \[ s^2 = r^2 + t^2 - 2rt \cdot \cos(S) \]3. Substitute the known values: \[ 5.6^2 = 3.9^2 + 6.1^2 - 2 \cdot 3.9 \cdot 6.1 \cdot \cos(S) \]4. Calculate each term: \[ 31.36 = 15.21 + 37.21 - 2 \cdot 3.9 \cdot 6.1 \cdot \cos(S) \] \[ 31.36 = 52.42 - 47.58 \cdot \cos(S) \]5. Isolate \( \cos(S) \): \[ 31.36 - 52.42 = - 47.58 \cdot \cos(S) \] \[ -21.06 = - 47.58 \cdot \cos(S) \] \[ \cos(S) = \frac{21.06}{47.58} \] \[ \cos(S) \approx 0.4427 \

Name: **Trigonometry Problem: Using the Law of Cosines to Find an Angle**In
Uploaded: 2024-03-20T06:47:08.000Z
Channel: Bartleby
Description: **Trigonometry Problem: Using the Law of Cosines to Find an Angle**In the given triangle \( \Delta RST \), the side lengths are as follows: \( r = 3.9 \) inches, \( s = 5.6 \) inches, and \( t = 6.1 \) inches.To find the measure of angle \( \angle S