If in an oblique △ABC , side a=23 ft , side b=17 ft , and m∠C=24° , then what is the length of side c to the nearest foot?(1 point)
Using the Law of Sines, we can set up the following ratio:
sin A / a = sin B / b = sin C / c
We are given that side a = 23 ft, side b = 17 ft, and ∠C = 24°. Let's solve for side c:
sin A / 23 = sin B / 17 = sin 24° / c
sin A = sin (180° - A - C) = sin (180° - 24° - B) = sin(156° - B) = sin B
Let x = sin A / 23 = sin B / 17 = sin 24° / c
sin 24° = sin 24°
sin 24° = 17 * sin 24° / c
c = 17 / sin 24° ≈ 41 ft
Therefore, the length of side c is approximately 41 feet.