Question

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

Explanation:

Step1: Identify the trigonometric ratio

In right - triangle \( \triangle UVT\), we know the side \(UV = 7\) (opposite side to angle \(T\)) and we want to find \(TV\) (adjacent side to angle \(T\)). The trigonometric ratio that relates the opposite and adjacent sides of a right - triangle is the tangent ratio. The formula for the tangent of an angle in a right - triangle is \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 67^{\circ}\), the opposite side \(opp = UV = 7\), and the adjacent side \(adj=TV\). So, \(\tan(67^{\circ})=\frac{UV}{TV}\).

Step2: Solve for \(TV\)

We can rewrite the formula \(\tan(67^{\circ})=\frac{7}{TV}\) as \(TV=\frac{7}{\tan(67^{\circ})}\). We know that \(\tan(67^{\circ})\approx2.356\). Then \(TV=\frac{7}{2.356}\approx3.0\).

Answer:

\(3.0\)