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Chapter 5: Problem 13

Use the Law of Sines to solve the triangle. Round your answers to two decimal places. $$A=35^{\circ}, \quad B=65^{\circ}, \quad c=10$$

Short Answer

Expert verified
After carrying out the mentioned steps, values for the respective sides a and b should be obtained after rounding to two decimal places. Since the exact calculation depends on the numerical approximation used, the exact numbers might vary slightly.

Step by step solution

01

Calculate the Third Angle

Since the measures of the angles in a triangle always sum to 180 degrees, we can find the measure of the last angle as follows: \[ C = 180 - A - B = 180 - 35 - 65 = 80^{\circ} \]
02

Use the Law of Sines to Solve for a

The Law of Sines allows us to say \[ \frac{a}{\sin(A)} = \frac{c}{\sin(C)} \] Substitute known values. Then solve for a: \[ a = \frac{c \cdot \sin(A)}{\sin(C)} = \frac{10 \cdot \sin(35^{\circ})}{\sin(80^{\circ})} \] Round the answer to two decimal places.
03

Use the Law of Sines to Solve for b

Following the same process to solve for b, using the Law of Sines \[ \frac{b}{\sin(B)} = \frac{c}{\sin(C)} \]\[ b = \frac{c \cdot \sin(B)}{\sin(C)} = \frac{10 \cdot \sin(65^{\circ})}{\sin(80^{\circ})} \] Round the answer to two decimal places.

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