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Chapter 5: Problem 16

Use the Law of Sines to solve the triangle. Round your answers to two decimal places. $$B=28^{\circ}, \quad C=104^{\circ}, \quad a=3 \frac{5}{8}$$

Short Answer

Expert verified
The third angle is 48掳. The length of the sides 'b' and 'c' are the results from Step 2 and Step 3, respectively. Remember to round your answers to two decimal places.

Step by step solution

01

Calculate the third angle

As the sum of the angles in a triangle equals 180掳, we can calculate the third angle A using the formula: A = 180掳 - B - C. Substitute B with 28掳 and C with 104掳, the angle A becomes A = 180掳 - 28掳 - 104掳 = 48掳.
02

Use Law of Sines to calculate the side c

Using the law of sines, we get \(\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}\) . We can rearrange this to find 'c': \(c = \sin C* \frac{a}{\sin A}\). Once we substitute the given numbers and our previous result for angle A into this formula: \(c = \sin (104掳)*\frac{3 5/8}{\sin (48掳)}\). Calculate this to get the side 'c' value.
03

Use Law of Sines to calculate the side b

We repeat Step 2 to find the side 'b'. This time, we use the formula: \(b = \sin B* \frac{a}{\sin A}\). Plugging in the values, we get: \(b = \sin (28掳)*\frac{3 5/8}{\sin (48掳)}\). Calculate this to get the side 'b' value.

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