Find a side using tangent
Objective. Use tangent to calculate an unknown side.
- 1. Learn
- 2. Worked example
- 3. Practice
- 4. Feedback
- 5. Continue
Learn: the key idea
Finding a missing side using tangent involves identifying the opposite and adjacent sides relative to a known angle in a right-angled triangle, then rearranging tan(θ) = opposite ÷ adjacent to solve for the unknown length. If the opposite side is unknown, multiply the adjacent side by tan(θ); if the adjacent side is unknown, divide the opposite side by tan(θ). For example, if the angle is 35° and the adjacent side is 12 cm, the opposite side is 12 × tan(35°) ≈ 8.40 cm. Always check with a calculator in degree mode before computing the tangent value.
Worked example
A right-angled triangle has an angle of 25° and the side adjacent to it is 14 cm. Find the length of the opposite side using tangent.
- 1Use the formula tan(θ) = opposite ÷ adjacent.
- 2Rearrange to find the opposite side: opposite = adjacent × tan(θ).
- 3Substitute the values: opposite = 14 × tan(25°).
- 4Using tan(25°) ≈ 0.466, opposite ≈ 14 × 0.466 ≈ 6.53 cm.
Answer: Approximately 6.53 cm
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Practice
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Start practisingCommon mistake. Pupils often divide instead of multiply when finding an opposite side from an adjacent side and an angle, applying the wrong rearrangement of the tangent formula. Carefully rearrange tan(θ) = opposite ÷ adjacent based on which side is actually unknown.
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