Right triangle upper A upper B upper C has a small square box at angle B. The side opposite of each angle is labeled as the lowercase letter of the angle name.
Use the Law of Sines to solve the following problem. If ∠C=35 degrees
and side c=42 yd.
, how long is side a to the nearest yard?
(1 point)
Responses
64 yd.
64 yd.
29 yd.
29 yd.
43 yd.
43 yd.
60 yd.
60 yd.
To solve for side a using the Law of Sines, we can use the formula:
a/sin(A) = c/sin(C)
Plugging in the values we know:
a/sin(B) = 42/sin(35)
Now we need to find sin(B), which can be calculated using the fact that the sum of angles in a triangle is 180 degrees:
180 - 90 - 35 = 55
sin(55) = a/42
a = 42sin(55)
a ≈ 60 yards
Therefore, side a is approximately 60 yards. So the answer is:
60 yd.