Question

brian wants to fence in his triangular plot of farm land that measures 1.1 by 1.5 by 2.2 miles. determine the angles at which the fences of the three sides will meet. rounding each angle to the nearest degree: ( mangle aapprox115 ) degrees complete ( mangle bapprox ) degrees done

Explanation:

Step1: Use the Law of Cosines

The Law of Cosines formula is \(c^{2}=a^{2}+b^{2}-2ab\cos C\). Let \(a = 1.1\), \(b=1.5\), \(c = 2.2\). First, we found \(\angle A\) (opposite side \(a = 2.2\)): \(2.2^{2}=1.1^{2}+1.5^{2}-2\times1.1\times1.5\times\cos A\). Solving for \(\cos A\): \(\cos A=\frac{1.1^{2}+1.5^{2}-2.2^{2}}{2\times1.1\times1.5}\approx - 0.427\), \(A=\cos^{-1}(-0.427)\approx115^{\circ}\). Now for \(\angle B\) (opposite side \(b = 1.1\)): \(1.1^{2}=1.5^{2}+2.2^{2}-2\times1.5\times2.2\times\cos B\). Then \(\cos B=\frac{1.5^{2}+2.2^{2}-1.1^{2}}{2\times1.5\times2.2}=\frac{2.25 + 4.84-1.21}{6.6}=\frac{5.88}{6.6}\approx0.891\).

Step2: Find \(\angle B\)

\(B=\cos^{-1}(0.891)\approx27^{\circ}\)

Answer:

\(27\)