If in an oblique △ABC , side a=17 ft., side b=20 ft., and ∠C=19 degrees, then what is the length of side c to the nearest foot?
To find the length of side c, we can use the Law of Sines, which states:
a/sin A = b/sin B = c/sin C
Here, we are given side a=17 ft., side b=20 ft., and ∠C=19 degrees.
We can find the measure of angle A using the fact that the sum of angles in a triangle is 180 degrees:
∠A = 180 - ∠B - ∠C
∠A = 180 - 90 - 19
∠A = 71 degrees
Now we can use the Law of Sines to find the length of side c:
17/sin(71) = 20/sin(90) = c/sin(19)
17/sin(71) = c/sin(19)
c = (17/sin(71)) * sin(19)
c ≈ (17/0.9511) * 0.3249
c ≈ 17.871 * 0.3249
c ≈ 5.81 ft.
Therefore, the length of side c to the nearest foot is approximately 6 ft.