Question

find tu.
triangle with right angle at u, angle at t is 56 degrees, length of uv is 3. write your answer as an integer or as a decimal rounded to the nearest tenth. tu = blank submit

Explanation:

Step1: Identify triangle type and trigonometric ratio

This is a right - triangle \( \triangle TUV \) with \( \angle U = 90^{\circ} \), \( \angle T=56^{\circ} \), and \( UV = 3 \). We want to find \( TU \). We can use the tangent function. Recall that in a right - triangle, \( \tan\theta=\frac{\text{opposite}}{\text{adjacent}} \). For \( \angle T \), the opposite side to \( \angle T \) is \( UV \) and the adjacent side is \( TU \). So \( \tan(56^{\circ})=\frac{UV}{TU} \).

Step2: Solve for \( TU \)

We know that \( UV = 3 \) and \( \tan(56^{\circ})\approx1.4826 \). From \( \tan(56^{\circ})=\frac{3}{TU} \), we can re - arrange the formula to solve for \( TU \): \( TU=\frac{3}{\tan(56^{\circ})} \). Substitute \( \tan(56^{\circ})\approx1.4826 \) into the formula: \( TU=\frac{3}{1.4826}\approx2.0 \) (rounded to the nearest tenth).

Answer:

\( 2.0 \)