Question

find v.
write your answer as an integer or as a decimal rounded to the nearest tenth.
v =
submit
work it out
not feeling ready yet? these can help:

Explanation:

Step1: Apply the Law of Cosines

The Law of Cosines states that for a triangle with sides \(a\), \(b\), \(c\) and the angle \(C\) opposite side \(c\), \(c^{2}=a^{2}+b^{2}-2ab\cos C\). In triangle \(XVW\), let \(a = 8\), \(b=15\), \(C = 104^{\circ}\), and \(c = v\). Then \(v^{2}=8^{2}+15^{2}-2\times8\times15\times\cos(104^{\circ})\).

Step2: Calculate each term

First, \(8^{2}=64\), \(15^{2}=225\). Then, \(\cos(104^{\circ})\approx - 0.2419\). So \(2\times8\times15\times\cos(104^{\circ})\approx2\times8\times15\times(- 0.2419)=- 58.056\).

Step3: Find \(v^{2}\)

\(v^{2}=64 + 225-(-58.056)=64+225 + 58.056=347.056\).

Step4: Find \(v\)

Take the square - root of \(v^{2}\), \(v=\sqrt{347.056}\approx18.6\).

Answer:

\(18.6\)