GCSE Maths Practice: trigonometry

Question 4 of 10

This question focuses on using tangent to find an angle when opposite and adjacent sides are known.

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\( \begin{array}{l}\text{How would you find an angle if you know opposite and adjacent sides?}\end{array} \)

Choose one option:

Identify opposite and adjacent sides clearly. Use \(\tan^{-1}\).

Tangent of an angle is defined as \(\tan \theta = \frac{\text{opposite}}{\text{adjacent}}\). If the lengths of opposite and adjacent sides are known, the angle can be found using \(\theta = \tan^{-1}(\text{opposite}/\text{adjacent})\). This is crucial in problems where the hypotenuse is unknown. Always label sides of the triangle and ensure the calculator is in degree mode. Practice finding angles using tangent in various triangles to strengthen understanding. Understanding tangent enables solving problems like building ramps, angles of elevation, and engineering applications. Rechecking results by substituting back into the formula helps verify correctness.