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Chapter 6: Problem 14

Solve each triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. $$B=5^{\circ}, C=125^{\circ}, b=200$$

Short Answer

Expert verified
An estimate of the solution is: angle A has approximate value of 32 degrees, angle C has approximate value of 93 degrees and side 'b' has approximate length of 6.4 units. Make sure to check the calculation and rounding off in accordance with the requirements of the task.

Step by step solution

01

Calculate Angle A using the Law of Sines

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 constant. So, \( \sin(A) = \frac{a}{c} \times \sin(B) \). Substituting the given values, \( \sin(A) = \frac{4}{7} \times \sin(55^{\circ}) \) . To get Angle A, take the \( \arcsin \) of the obtained value.
02

Calculate Angle C

The angles in a triangle sum up to 180 degrees. Knowing this, Angle C can be found using the formula \( C = 180^{\circ} - B - A \). Substitute the given value for B and the calculated value of A into the equation and compute the result.
03

Find the length of side 'b' using the Law of Sines

With all angles solved, we can find the length of side 'b' again using the Law of Sines. This time, \( b = c \times \frac{\sin(B)}{\sin(C)} \). Substitute the given values and the calculated value of C into the equation to solve for 'b'.

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