Question

find the value of x. round your answer to two decimal places. enter deg after any degree value.
triangle rts with right angle at t, angle at r is 22°, rt = 17, rs = x

Explanation:

Step1: Identify trigonometric ratio

In right triangle \( RTS \), \( \angle R = 22^\circ \), adjacent side to \( \angle R \) is \( RT = 17 \), and hypotenuse is \( x \). We use cosine: \( \cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}} \), so \( \cos(22^\circ)=\frac{17}{x} \).

Step2: Solve for \( x \)

Rearrange the formula: \( x = \frac{17}{\cos(22^\circ)} \). Calculate \( \cos(22^\circ)\approx0.9272 \), then \( x=\frac{17}{0.9272}\approx18.33 \).

Answer:

\( 18.33 \)