Final answer:
To find the length of side l (LM), we calculate angle N (10°) using the angle sum property of triangles, then apply the Law of Sines with the known angles and side n (NM), and round the result to the nearest centimeter.
Step-by-step explanation:
The student is asking for the length of side l (LM) in triangle LMN, where we know the length of side n (NM) is 960 cm, and the measures of angles L and M are 160° and 10°, respectively. Since the sum of angles in a triangle equals 180°, we can find angle N by subtracting the sum of angles L and M from 180°. This gives us:
∠N = 180° - (∠L + ∠M) = 180° - (160° + 10°) = 10°.
Now we can use the Law of Sines which states that the ratio of the length of a side to the sine of its opposite angle is the same for all sides of the triangle:
ℓ/℘(∠L) = n/℘(∠N)
l/℘(160°) = 960/℘(10°)
By solving for l, we get:
l = 960 × ℘(160°) / ℘(10°)
After calculating using a calculator, we round the answer to the nearest centimeter for the student's request