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Chapter 5: Problem 18

Use the Law of Cosines to solve the triangle. Round your answers to two decimal places. $$C=15^{\circ} 15^{\prime}, \quad a=7.45, \quad b=2.15$$

Short Answer

Expert verified
By applying the Law of Cosines and Law of Sines correctly, one would be able to resolve the given triangle. The exact values of side c and angles A and B would depend on the specific calculations performed.

Step by step solution

01

Introduction of Law of Cosines

The Law of Cosines in a triangle is given by the equation:\[c^2 = a^2 + b^2 - 2ab \cos(C)\] where \(a\), \(b\) and \(c\) are the sides of the triangle, and \(C\) is the angle included by \(a\) and \(b\). The values \(a=7.45\), \(b=2.15\) and \(C=15^{\circ} 15^{\prime}\) are given.
02

Calculate side c

Let鈥檚 calculate side \(c\) using the formula above. But before plugging the numbers, we need to convert the angle \(C\) from degrees and minutes to decimal degrees. We have \(15^{\circ} 15^{\prime} = 15 + 15/60 = 15.25^\circ\). Now use the values \(a=7.45\), \(b=2.15\) and \(C=15.25^\circ\) in the law of cosines to find \(c\).
03

Calculate the remaining angles A and B

To find the other angles \(A\) and \(B\), we use the Law of Sines. This law states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all sides and angles in a given triangle. Thus we have \(\dfrac{sin A}{a} = \dfrac{sin B}{b} = \dfrac{sin C}{c}\). Let's use this to calculate angles \(A\) and \(B\).

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