In a right triangle with a 60° angle, if the side adjacent to the angle measures 7 inches, what is the length of the opposite side?

To find the length of the side opposite the 60° angle in a right triangle when the adjacent side measures 7 inches, trigonometric ratios can be applied. Specifically, we use the tangent function, which is defined as the ratio of the length of the opposite side to the length of the adjacent side.

In this scenario, the tangent of 60° can be expressed mathematically as:

[

\tan(60°) = \frac{\text{opposite}}{\text{adjacent}}

]

Given that the length of the adjacent side is 7 inches, we represent the opposite side as ( x ). Thus, the equation becomes:

[

\tan(60°) = \frac{x}{7}

]

Knowing that ( \tan(60°) = \sqrt{3} ) (approximately 1.732), we can substitute this value into the equation:

[

\sqrt{3} = \frac{x}{7}

]

To solve for ( x ), multiply both sides by 7:

[

x = 7 \cdot \sqrt{3}

]

Calculating ( 7 \cdot \sqrt{3} ):

If ( \sqrt