Question

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

Explanation:

Step1: Use trigonometric ratio

In right - triangle \(UST\), \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 54^{\circ}\), the opposite side to \(\theta\) is \(US = 7\), and the adjacent side is \(ST\). So, \(\tan(54^{\circ})=\frac{US}{ST}\).

Step2: Solve for \(ST\)

Since \(\tan(54^{\circ})\approx1.376\) and \(\tan(54^{\circ})=\frac{7}{ST}\), then \(ST=\frac{7}{\tan(54^{\circ})}\).
Substitute \(\tan(54^{\circ})\approx1.376\) into the formula: \(ST=\frac{7}{1.376}\approx5.1\)

Answer:

\(5.1\)