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?
62 m
53 m
15 m
25 m
To solve for side a, we can use the Law of Sines, which states that the ratio of a side length to the sine of its opposite angle is constant for all sides and their opposite angles in a triangle.
In this example, we know that ∠C = 28 degrees and side c = 28 m.
We can set up the equation using the Law of Sines:
sin(A) / a = sin(C) / c
Plugging in the values we know:
sin(A) / a = sin(28) / 28
Next, we can solve for sin(A):
sin(A) = (sin(28) * a) / 28
To solve for a, we can rewrite the equation:
a = (28 * sin(A)) / sin(28)
However, we don't currently know the value of angle A. To find it, we can use the fact that the sum of the angles in a triangle is 180 degrees:
A + B + C = 180
Since we know ∠C = 28 degrees, we can solve for angle B:
B = 180 - A - C
B = 180 - A - 28
B = 152 - A
Now, we can use the fact that the sum of the angles in a triangle is 180 degrees to solve for angle A:
A + B + C = 180
A + (152 - A) + 28 = 180
152 + 28 = 180
180 = 180
Therefore, we know that A = 152 degrees.
Now we can substitute the values of sin(28), sin(A), and sin(152) into the equation for a:
a = (28 * sin(152)) / sin(28)
Using a calculator to approximate the values of sin(28) and sin(152), we get:
a ≈ (28 * 0.469) / 0.469
a ≈ 28
Therefore, side a is approximately 28 m. Answer: 28 m.