Question

find c if a = 2.15 mi, b = 3.11 mi and ∠c = 40.2 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 submit question

Explanation:

Step1: Apply the Law of Cosines

The Law of Cosines formula is \(c^{2}=a^{2}+b^{2}-2ab\cos C\).
Given \(a = 2.15\), \(b = 3.11\), and \(C=40.2^{\circ}\).
First, calculate \(a^{2}=(2.15)^{2}=4.6225\), \(b^{2}=(3.11)^{2}=9.6721\), and \(2ab = 2\times2.15\times3.11 = 13.473\).
\(\cos(40.2^{\circ})\approx0.76397\).

Step2: Substitute values into the formula

\(c^{2}=4.6225 + 9.6721-13.473\times0.76397\).
\(c^{2}=4.6225+9.6721 - 10.303\).
\(c^{2}=3.9916\).

Step3: Solve for \(c\)

Take the square root of \(c^{2}\), \(c=\sqrt{3.9916}\approx1.998\).

Answer:

\(1.998\)