Final answer:
To find the length of side b in the triangle, use the law of sines with the known angle and side values to calculate b. Apply the formula b = a × (sin(B) / sin(A)), input the respective angles, and compare the calculated value to the given choices to find the approximate length.
Step-by-step explanation:
The triangle problem can be solved by knowing that the sum of angles in any triangle is 180 degrees. Given that m∠a is 107° and m∠c is 24°, we can calculate the missing angle m∠b which is 180° - (107° + 24°) = 49°. To find the approximate length of side b, we can use the law of sines which states that ratio of the length of a side to the sine of its opposite angle is the same for all sides of a triangle: (a / sin(A)) = (b / sin(B)) = (c / sin(C)). Since we have a = 44 ft and its opposite angle A is 107°, and we want to find b for which the opposite angle B is 49°, using the law of sines gives us:
b = a × (sin(B) / sin(A)) = 44 ft × (sin(49°) / sin(107°))
By calculating this, we get the approximate answer for the length of side b. The answer choices give us the suggestion that the length of b would be around the lengths given as options, so using a calculator for the above expression should yield a value that is close to one of the options provided.