Use the Law of Sines to solve the following problem. If ∠C=28 degrees and side c=28 m , then what is the length of side a to the nearest meter?
15 m
15 m
53 m
53 m
25 m
25 m
62 m
To use the Law of Sines, we can set up the following proportion:
sin(A) / a = sin(C) / c
Plugging in the given values, we have:
sin(A) / a = sin(28°) / 28
To solve for a, we can cross-multiply and isolate a:
a = (28 * sin(A)) / sin(28°)
Since we don't have enough information to directly calculate a, we need to find the value of sin(A). Since the sum of angles in a triangle is 180°, we can find angle A by subtracting angles B and C from 180°:
A = 180° - B - C
A = 180° - 90° - 28°
A = 62°
Now we can substitute this value back into our equation for a:
a = (28 * sin(62°)) / sin(28°)
Using a calculator, we find that sin(62°) ≈ 0.8829 and sin(28°) ≈ 0.4695:
a ≈ (28 * 0.8829) / 0.4695
a ≈ 52.05
Rounding to the nearest meter, the length of side a is approximately 52 m.