Question

annas triangle
95°
40°
45°
carleys triangle
yunas triangle
4.1 cm
4.4 cm
3.6 cm
sakis triangle
which triangle can be solved using only the law of cosines?
○ annas triangle
○ yunas triangle
○ carlys triangle
○ sakis triangle

Explanation:

The Law of Cosines is used when we know all three sides of a triangle (SSS) or two sides and the included angle (SAS). Let's analyze each triangle:

• Anna’s triangle: Has angle - angle - angle (AAA) information. We can't use the Law of Cosines directly here as we need side - related information. We would use the Law of Sines or triangle angle - sum property first to find relationships, but not just Law of Cosines.
• Yuna’s triangle: We know two sides and a non - included angle? Wait, no, looking at the diagram, Yuna's triangle: Wait, the labels are a bit confusing. Wait, Saki's triangle: Wait, Saki's triangle has three sides: 4.4 cm, 3.6 cm, and 4.1 cm? Wait, no, let's re - examine.

Wait, Saki's triangle: The sides are 4.4 cm, 3.6 cm, and the base is 4.1 cm? Wait, no, the correct analysis:

• Saki’s triangle: If we know all three sides (SSS), we can use the Law of Cosines to find any angle. The Law of Cosines formula for a triangle with sides \(a\), \(b\), \(c\) and opposite angles \(A\), \(B\), \(C\) is \(c^{2}=a^{2}+b^{2}-2ab\cos(C)\), \(a^{2}=b^{2}+c^{2}-2bc\cos(A)\), \(b^{2}=a^{2}+c^{2}-2ac\cos(B)\). So if we know all three sides, we can solve for the angles using the Law of Cosines.
• Anna’s triangle: Has angles, so we would use Law of Sines (since we can find ratios of sides) or triangle angle - sum.
• Yuna’s triangle: If we assume it's two sides and a non - included angle (or maybe not, but from the diagram, Saki's triangle has three sides given (4.4, 3.6, 4.1), so SSS case, which is solvable by Law of Cosines.

Answer:

Saki’s triangle