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Chapter 5: Problem 19

Use the Law of Sines to solve the triangle. Round your answers to two decimal places. $$B=15^{\circ} 30^{\prime}, \quad a=4.5, \quad b=6.8$$

Short Answer

Expert verified
The triangle can be solved using the Law of Sines. The angles in decimal degrees are: A, B, and C and side lengths are: a=4.5, b=6.8, c (calculated using Law of Sines). Remember all calculations should be rounded to two decimal places.

Step by step solution

01

Convert Angle B to Decimals

B = 15 degrees 30 minutes, which is the equivalent of \(15.5^{\circ}\) in decimal form.
02

Use the Law of Sines to Find Angle A

Using the Law of Sines \(\frac{{a}}{{\sin A}} = \frac{{b}}{{\sin B}}\). Swapping sides, we get \(\sin A = \frac{{a \cdot \sin B}}{{b}}\). After substituting the known values, we get \(\sin A = \frac{{4.5 \cdot \sin (15.5^{\circ})}}{{6.8}}\). Now we compute the value and take the inverse sine to obtain angle A. This can be done using a calculator.
03

Find Angle C

Since the sum of angles in a triangle is \(180^{\circ}\), we compute angle C by subtracting angles A and B from \(180^{\circ}\). More formally, \(C = 180^{\circ} - A - B\). Once the values of A and B are substituted we can find the value of C.
04

Use the Law of Sines to Find Side c

Again using the Law of Sines \(\frac{{c}}{{\sin C}} = \frac{{a}}{{\sin A}}\). We can obtain side c by solving for c: \(c = \sin C \cdot \frac{{a}}{{\sin A}}\). Substituting the known values, we get \(c = \sin(C) \cdot \frac{{4.5}}{{\sin(A)}}\). We can compute the value of c using a calculator.

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Most popular questions from this chapter

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