Question

find c if a = 2.42 mi, b = 3.93 mi and ∠c = 40.8 degrees. enter c rounded to 3 decimal places. c = mi; assume ∠a is opposite side a, ∠b is opposite side b, and ∠c is opposite side c. question help: video

Explanation:

Step1: Apply the Law of Cosines

The Law of Cosines formula is \(c^{2}=a^{2}+b^{2}-2ab\cos C\).
Given \(a = 2.42\), \(b = 3.93\), and \(C=40.8^{\circ}\).
First, calculate \(a^{2}=(2.42)^{2}=5.8564\), \(b^{2}=(3.93)^{2}=15.4449\), and \(2ab = 2\times2.42\times3.93=19.0092\), \(\cos(40.8^{\circ})\approx0.757\).

Step2: Substitute values into the formula

\(c^{2}=5.8564 + 15.4449-19.0092\times0.757\).
\(c^{2}=5.8564+15.4449 - 14.390\).
\(c^{2}=6.9113\).

Step3: Solve for \(c\)

Take the square - root of both sides: \(c=\sqrt{6.9113}\approx2.629\).

Answer:

\(2.629\)