To solve this problem, we can use the Law of Sines, which states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant.
In this case, we know that angle C is 38° and side c is 22 mi.
Using the Law of Sines, we can set up the following equation:
sin(A)/a = sin(C)/c
Plugging in the known values:
sin(A)/a = sin(38°)/22
To find side a, we want to isolate it on one side of the equation. We can do this by multiplying both sides by a:
sin(A) = a*sin(38°)/22
Now, to solve for a, we can take the inverse sine (or arcsine) of both sides:
A = arcsin(a*sin(38°)/22)
Using a calculator, we find that A is approximately 23.46°.
Now, we can use the fact that the sum of the angles in a triangle is 180° to find angle B:
B = 180° - A - C
B = 180° - 23.46° - 38°
B = 118.54°
Finally, we can use the Law of Sines again to find side a:
sin(A)/a = sin(B)/b
sin(23.46°)/a = sin(118.54°)/b
To find side a, we can rearrange the equation and solve for it:
a = b*sin(23.46°)/sin(118.54°)
Plugging in the known values:
a = 22*sin(23.46°)/sin(118.54°)
Using a calculator, we find that a is approximately 17 mi.
Therefore, the length of side a to the nearest mile is 17 mi.
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?
17 mi.
17 mi.
28 mi.
28 mi.
32 mi.
32 mi.
49 mi.
1 answer