The image shows a triangle problem where the Law of Sines is being used to find unknown angles or sides of a triangle.

Here’s a breakdown of the triangle and the provided information:

• Angle $A = 41^\circ$
• Angle $C = 27^\circ$
• Side $AC = 3.4$ (opposite angle $B$)

The Law of Sines formula is written on the screen as: $\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$ Where:

• $a$, $b$, and $c$ are the lengths of the sides opposite to angles $A$, $B$, and $C$, respectively.
• $A$, $B$, and $C$ are the angles of the triangle.

Steps to solve:

1. Find Angle $B$: Using the triangle angle sum property: $A + B + C = 180^\circ$ Substituting the known values: $41^\circ + B + 27^\circ = 180^\circ$ Simplifying: $B = 180^\circ - 41^\circ - 27^\circ = 112^\circ$

2. Use the Law of Sines to find missing sides: You can now apply the Law of Sines to solve for unknown sides if needed. For example, to find side $a$, you could use: $\frac{a}{\sin 41^\circ} = \frac{3.4}{\sin 112^\circ}$ And to find side $c$, you can use: $\frac{c}{\sin 27^\circ} = \frac{3.4}{\sin 112^\circ}$

Would you like to proceed with solving for the sides, or is there a particular step you'd like to focus on?

Related Questions:

1. How do we use the Law of Sines to find unknown angles?
2. Can we apply the Law of Cosines to this triangle?
3. Why is the sum of angles in a triangle always $180^\circ$?
4. How do we solve for side lengths using trigonometric ratios?
5. What happens if the triangle is obtuse or right-angled when using the Law of Sines?

Tip:

Always remember to ensure that the angles and sides are correctly paired when using the Law of Sines to avoid errors in calculations.