Question

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

Explanation:

Step1: Identify the triangle type and trigonometric ratio

We have a right - triangle \( \triangle RST \) with \( \angle S = 90^{\circ} \), \( \angle T=24^{\circ} \), and the hypotenuse \( RT = 5 \). We want to find the length of \( ST \), which is the adjacent side to the angle \( \angle T \). The cosine of an angle in a right - triangle is defined as \( \cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}} \). So, \( \cos(24^{\circ})=\frac{ST}{RT} \).

Step2: Substitute the known values and solve for \( ST \)

We know that \( RT = 5 \) and \( \theta = 24^{\circ} \). Substituting these values into the cosine formula, we get \( ST=RT\times\cos(24^{\circ}) \).
We calculate \( \cos(24^{\circ})\approx0.9135 \). Then \( ST = 5\times0.9135 = 4.5675 \). Rounding to the nearest tenth, we get \( ST\approx4.6 \).

Answer:

\( 4.6 \)