How to Find an Angle in a Right Triangle Given All Three Sides

Learn how to calculate an angle in a right triangle using all three sides with the cosine rule and arccosine function.

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To find an angle in a right triangle when you know all three sides, use the cosine rule. For angle θ, the formula is θ = arccos((adjacent side) / hypotenuse). For angle Φ, use Φ = arccos((opposite side) / hypotenuse). Use a calculator to find the arccosine value.

FAQs & Answers

  1. What formula is used to find an angle in a right triangle when all sides are known? You use the cosine rule, specifically the arccosine function of the adjacent or opposite side divided by the hypotenuse.
  2. Can I use the sine or tangent functions if I know all three sides? While sine and tangent are useful when certain sides or angles are known, the cosine rule with arccosine is best when all three sides are given.
  3. How do I calculate the arccosine on my calculator? Use the inverse cosine (cos⁻¹ or arccos) function on your scientific calculator after inputting the ratio of the known side over the hypotenuse.