Question

find the value of each variable.
1.
right triangle with right angle, hypotenuse 18, angle 25° at the base, vertical leg t, horizontal leg s

Explanation:

Step1: Identify trigonometric ratios

We have a right triangle with hypotenuse \( 18 \), angle \( 25^\circ \). For side \( t \) (opposite to \( 25^\circ \)): use \( \sin\theta=\frac{\text{opposite}}{\text{hypotenuse}} \), so \( \sin(25^\circ)=\frac{t}{18} \), then \( t = 18\sin(25^\circ) \). For side \( s \) (adjacent to \( 25^\circ \)): use \( \cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}} \), so \( \cos(25^\circ)=\frac{s}{18} \), then \( s = 18\cos(25^\circ) \).

Step2: Calculate values

Using calculator, \( \sin(25^\circ)\approx0.4226 \), so \( t\approx18\times0.4226\approx7.607 \). \( \cos(25^\circ)\approx0.9063 \), so \( s\approx18\times0.9063\approx16.313 \).

Answer:

\( t \approx 7.61 \), \( s \approx 16.31 \) (or more precise values based on calculator precision)