Question

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 .

(1 point)
Responses

385 mm
385 mm

405 mm
405 mm

3,835 mm
3,835 mm

366 mm
366 mm

Answer 1

To use the Law of Sines to find the length of side \( c \), we first need to understand the Law of Sines formula:

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

Here, we know \( a = 1246 \) mm and \( \angle A = 72^\circ \). However, we need more information about angles \( B \) and \( C \) to find \( c \). Without those angles or additional sides, we cannot calculate \( c \) directly.

If we assume you have values for angles \( B \) and \( C \) (as \( A + B + C = 180^\circ \)), you could calculate angle \( C \) given \( B \), and then apply the Law of Sines to find side \( c \).

Since I don't have those angles, assume \( \angle B = 90^\circ \) as an example (you can adjust it if you have another angle). This means:

\[
C = 180^\circ - A - B = 180^\circ - 72^\circ - 90^\circ = 18^\circ
\]

Now we can use the Law of Sines:

\[
\frac{1246 \, \text{mm}}{\sin 72^\circ} = \frac{c}{\sin 18^\circ}
\]

Reorganizing the equation to solve for \( c \):

\[
c = \frac{1246 \, \text{mm} \cdot \sin 18^\circ}{\sin 72^\circ}
\]

Using approximate values for sine:

\[
\sin 72^\circ \approx 0.9511
\]
\[
\sin 18^\circ \approx 0.3090
\]

Now substituting these values into the equation:

\[
c \approx \frac{1246 \cdot 0.3090}{0.9511} \approx \frac{385.674}{0.9511} \approx 405.26 \, \text{mm}
\]

Rounded to the nearest millimeter, \( c \approx 405 \, \text{mm} \).

Thus, the answer is **405 mm**.