Use the Law of Sines to solve the following problem. If ∠C
= 38° and side c
= 22mi., then how long is side a
to the nearest mile?
To solve this problem using the Law of Sines, we will refer to the triangle as ABC, where angle C is 38 degrees and side c is 22 miles.
The Law of Sines states that in any triangle, the ratio of the length of a side to the sine of the opposite angle is constant. Mathematically, it can be expressed as:
a / sin(A) = c / sin(C)
In this case, we want to find the length of side a, so we can rearrange the equation to solve for a:
a = (sin(A) * c) / sin(C)
Substituting the given values:
a = (sin(A) * 22) / sin(38°)
To calculate this expression, we need to know the measure of angle A. Without that information, we are unable to determine the length of side a using the Law of Sines.