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The problem involves determining the value of \( z \) in a right-angled triangle, where the given angle is \( 54^\circ \) and the opposite side length is 8 cm. The length \( z \) is the adjacent side to the angle \( 54^\circ \).

To solve for \( z \), we can use the trigonometric function tangent (tan), which relates the opposite side to the adjacent side in a right-angled triangle:

\[
\text{tan}(\theta) = \frac{\text{opposite}}{\text{adjacent}}
\]

Substituting the given values:

\[
\text{tan}(54^\circ) = \frac{8}{z}
\]

To solve for

Determine the value of z in the right-angled triangle where the given angle is 54° and the opposite side length is 8 cm. Provide the answer correct to 1 decimal place.

Learn how to determine the value of the adjacent side in a right-angled triangle using the trigonometric ratio tan(54°). Given an opposite side length of 8 cm, this problem walks through applying the tan formula and solving for the adjacent side. Ideal for students in Grades 9-10.

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