Question

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

Explanation:

Step1: Apply the Law of Cosines

The Law of Cosines formula is \(u^{2}=v^{2}+t^{2}-2vt\cos U\). Here, \(v = 9\), \(t = 13\), and \(U=50^{\circ}\). So, \(u^{2}=9^{2}+13^{2}-2\times9\times13\times\cos(50^{\circ})\).

Step2: Calculate each term

First, \(9^{2}=81\), \(13^{2}=169\). And \(\cos(50^{\circ})\approx0.6428\). Then \(2\times9\times13\times0.6428 = 2\times117\times0.6428=234\times0.6428 = 150.4152\).

Step3: Compute \(u^{2}\)

\(u^{2}=81 + 169-150.4152=250 - 150.4152 = 99.5848\).

Step4: Find \(u\)

Take the square - root of \(u^{2}\), \(u=\sqrt{99.5848}\approx9.98\approx10.0\).

Answer:

\(10.0\)