Mathematics

Mathematics

Problem

In a right-angled triangle, the side opposite a 60∘60^\circ angle measures 8 cm8\ \text{cm}. Calculate the length of the side adjacent to this angle, giving your answer to two decimal places.
Intuitive explanation

This is a trigonometric ratio problem where you need to connect a known side to an unknown side using the angle between them. Since you know the opposite side and want the adjacent side, the tangent ratio (tan⁡=oppositeadjacent\tan = \frac{\text{opposite}}{\text{adjacent}}) is your tool—rearrange it to solve for the unknown. Remember that tan⁡60°=3\tan 60° = \sqrt{3}, so you're really just doing a clean algebraic step.

Intuitive explanation

This is a trigonometric ratio problem where you need to connect a known side to an unknown side using the angle between them. Since you know the opposite side and want the adjacent side, the tangent ratio (tan⁡=oppositeadjacent\tan = \frac{\text{opposite}}{\text{adjacent}}) is your tool—rearrange it to solve for the unknown. Remember that tan⁡60°=3\tan 60° = \sqrt{3}, so you're really just doing a clean algebraic step.

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