Question

solve for x. round to the nearest tenth, if necessary.
triangle with right angle at t, angle at s is 72 degrees, side ut is 9.4, side su is x

Explanation:

Step1: Identify trigonometric ratio

In right triangle \( STU \), \( \angle S = 72^\circ \), \( UT = 9.4 \) (adjacent to \( \angle S \)), and \( SU = x \) (hypotenuse). We use cosine: \( \cos(72^\circ)=\frac{\text{adjacent}}{\text{hypotenuse}}=\frac{UT}{SU} \).

Step2: Substitute values

\( \cos(72^\circ)=\frac{9.4}{x} \), solve for \( x \): \( x = \frac{9.4}{\cos(72^\circ)} \).

Step3: Calculate \( \cos(72^\circ) \)

\( \cos(72^\circ)\approx0.3090 \).

Step4: Compute \( x \)

\( x=\frac{9.4}{0.3090}\approx30.4 \).

Answer:

\( 30.4 \)