Question

solve for x.
x = \square (round to the nearest hundredth.)
(the image shows a right triangle with right angle at c, angle at a is 39 degrees, side ac is 36, side bc is x)

Explanation:

Step1: Identify trigonometric ratio

In right triangle \( \triangle ABC \) (right-angled at \( C \)), we have angle \( 39^\circ \), adjacent side to the angle is \( 36 \), and opposite side is \( x \). So we use tangent function: \( \tan(\theta)=\frac{\text{opposite}}{\text{adjacent}} \)
\( \tan(39^\circ)=\frac{x}{36} \)

Step2: Solve for \( x \)

Multiply both sides by \( 36 \): \( x = 36\times\tan(39^\circ) \)
Calculate \( \tan(39^\circ)\approx0.8098 \)
\( x = 36\times0.8098 \approx 29.15 \)

Answer:

\( 29.15 \)