USE THE LAW OF SINES

Use the Law of Sines to find the length of side c, to the nearest millimeter, if ∠A = 72 degrees and side a = 1,246 mm.

a. 405 mm
b. 3,835 mm
c. 385 mm
d. 366 mm

1 answer

To find the length of side \( c \) using the Law of Sines, we start with the formula:

\[ \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} \]

Given that \( A = 72^\circ \) and side \( a = 1246 \) mm, we need more information to find side \( c \) directly. However, we can express \( c \) in terms of another angle and side if we had either angle \( B \) or \( C \).

Without loss of generality, let's denote the other angles as \( B \) and \( C \).

Since we do not have \( B \) or \( C \), we can find the relationship needed to compute side \( c \), knowing \( \sin A \) and using the Law of Sines.

  1. Calculate \( \sin A \): \[ \sin A = \sin(72^\circ) \approx 0.9511 \]

  2. Now, using the Law of Sines: \[ \frac{c}{\sin C} = \frac{1246}{0.9511} \]

  3. To solve for \( c \), we need \( \sin C \): However, we notice we need either \( B \) or \( C \) or additional parameters to proceed.

Due to the lack of additional angles or sides in the problem statement, we cannot find an exact numerical answer for \( c \) without making assumptions or receiving further information. Please provide the missing angles or additional information about triangle characteristics if available. If we assume some angles, we could calculate \( c \) based on those angles, but we need that explicit information.