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Chapter 5: Problem 20

Use the Law of Sines to solve the triangle. Round your answers to two decimal places. $$B=2^{\circ} 45^{\prime}, \quad b=6.2, \quad c=5.8$$

Short Answer

Expert verified
After performing all the calculations, the values for angle C, angle A and side a are obtained. These complete the measures of the triangle.

Step by step solution

01

Calculation of Angle C

Use the law of sines to find angle C. The Law of Sines states that the ratio of the length of a side of a triangle to the sine of its opposite angle is the same for all three sides and angles. Rearranging the formula and letting \( B = 2.75^{\circ} \) (which is \(2^{\circ} 45^{\prime}\) in decimal), we get: \(C = \arcsin(\frac{c}{b} * \sin(B))\) which is \(C = \arcsin(\frac{5.8}{6.2} * \sin(2.75))\). Calculate the value in the brackets first, then apply the arcsin.
02

Calculation of Angle A

After finding angle C, calculate the remaining angle, which is A. Since the sum of angles in a triangle equals 180, subtract the known angles from 180. The formula is \(A = 180 - B - C\). Substitute the known values and calculate.
03

Calculation of Side a

After getting all the angles, use the law of sines again to find side a. The formula is \(a = \frac{\sin(A)}{\sin(B)} * b\). Substitute the known values in to solve for a.

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