GCSE Maths Practice: trigonometry

Question 5 of 10

Use cosine to calculate a side length in a right-angled triangle when angle and hypotenuse are given.

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\( \begin{array}{l}\text{In a right-angled triangle, } \cos 60^\circ = \frac{x}{16}.\\ \text{Find } x.\end{array} \)

Choose one option:

Label sides carefully. Multiply hypotenuse by cosine.

Cosine relates the adjacent side to the hypotenuse: \(\cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}}\). When the angle is 60° and the hypotenuse is 16, multiply the hypotenuse by \(\cos 60^\circ = 0.5\) to get 8. This method applies to any right-angled triangle. Practice labeling sides correctly and using the formula. Knowing exact cosine values for standard angles (30°, 45°, 60°) helps speed up calculations. This is widely used in surveying, construction, and physics problems.