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?
The Law of Sines states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant. This can be written as:
a/sin(A) = c/sin(C)
where a is the length of side a, A is the measure of angle A, c is the length of side c, and C is the measure of angle C.
In this problem, we are given that ∠C = 28 degrees and c = 28 m. We need to find the length of side a.
Using the Law of Sines, we can set up the following equation:
a/sin(A) = 28/sin(28)
To solve for a, we can cross-multiply and solve for a:
a = (28*sin(A))/sin(28)
Now, we need to find the measure of angle A. Since the sum of the angles in a triangle is 180 degrees, we can find ∠A using the following equation:
∠A = 180 - ∠C - ∠B
Since we don't know ∠B, we can use the fact that it is an angle in a triangle to find its measure:
∠B = 180 - ∠A - ∠C
Substituting ∠C = 28 degrees, we have:
∠B = 180 - ∠A - 28
∠B = 152 - ∠A
Substituting this back into the equation for ∠A:
∠A = 180 - 28 - (152 - ∠A)
∠A = 152 + ∠A - 28
2∠A = 152 - 28
2∠A = 124
∠A = 62 degrees
Now we can substitute this value into the equation for a:
a = (28*sin(62))/sin(28)
Using a calculator, we find:
a ≈ 34 m
Therefore, the length of side a to the nearest meter is 34 meters.