Final answer:
To solve the triangle using the Law of Sines, we can use the equation sin(A)/a = sin(B)/b = sin(C)/c, where a, b, and c are the lengths of the sides opposite to angles A, B, and C respectively. Knowing the values of angle A and side c, we can find the lengths of sides a and b using this equation. By plugging in the values and solving for the unknowns, we can determine the lengths of all three sides of the triangle.
Step-by-step explanation:
To solve the triangle using the Law of Sines, we start by sketching the triangle with angle A measuring 23°, angle B measuring 110°, and side c measuring 50. Next, we can use the Law of Sines which states that the ratio of the sine of an angle to the length of the opposite side is constant for all angles in a triangle. Therefore, we can set up the equation: sin(A)/a = sin(B)/b = sin(C)/c, where a, b, c are the lengths of the sides opposite to angles A, B, C respectively.
Since we know the value of angle A and side c, we can find the value of side a by rearranging the equation: sin(A)/a = sin(B)/b. Plugging in the values, we get sin(23°)/a = sin(110°)/50. We can solve for a by cross multiplying and taking the reciprocal: a = (50 * sin(23°))/sin(110°). Calculating this value will give us the length of side a.
Similarly, we can find the length of side b using the equation: sin(A)/a = sin(B)/b. Plugging in the values, we get sin(23°)/a = sin(110°)/b. We can solve for b by cross multiplying and taking the reciprocal: b = (a * sin(110°))/sin(23°). Calculating this value will give us the length of side b.