Question

find v.
write your answer as an integer or as a decimal rounded to the nearest tenth.
v =
submit

Explanation:

Step1: Find angle at U

The sum of angles in a triangle is \(180^\circ\). So, \(\angle U = 180^\circ - 119^\circ - 18^\circ = 43^\circ\).

Step2: Apply the Law of Sines

The Law of Sines states that \(\frac{v}{\sin V}=\frac{VU}{\sin T}\). Here, \(VU = 3\), \(\angle V = 119^\circ\), \(\angle T = 18^\circ\). So, \(v=\frac{3\times\sin 119^\circ}{\sin 18^\circ}\).
Calculate \(\sin 119^\circ\approx\sin(180^\circ - 61^\circ)=\sin 61^\circ\approx0.8746\) and \(\sin 18^\circ\approx0.3090\).
Then \(v=\frac{3\times0.8746}{0.3090}\approx\frac{2.6238}{0.3090}\approx8.5\).

Answer:

\(8.5\)