Question

practice using the law of cosines.
in δdef, de = 11, ef = 9, and angle e = 140°.
which equation correctly uses the law of cosines to solve for the third side?
e² = 11² + 9² - 2(11)(9)cos(140°)
11² = e² + 9² - 2e(9)cos(140°)
9² = e² + 11² - 2e(11)cos(140°)
e = 11 + 9 - 2(11)(9)cos(140°)

Explanation:

Step1: Recall the law of cosines formula

The law of cosines formula is \( a^{2}=b^{2}+c^{2}-2bc\cos A\), where \(a\) is the side opposite angle \(A\), and \(b\) and \(c\) are the other two sides.

Step2: Identify the sides and angle in \(\triangle DEF\)

In \(\triangle DEF\), we want to find side \(e\). The sides adjacent to angle \(E\) are \(DE = 11\) and \(EF=9\), and angle \(E = 140^{\circ}\).
Substituting into the law of cosines formula (\(a = e\), \(b = 11\), \(c = 9\), \(A=140^{\circ}\)), we get \(e^{2}=11^{2}+9^{2}-2(11)(9)\cos(140^{\circ})\)

Answer:

\(e^{2}=11^{2}+9^{2}-2(11)(9)\cos(140^{\circ})\) (the first option)