Work out the value of x: Give your answer correct to 1 decimal place. - Edexcel - GCSE Maths - Question 6 - 2020 - Paper 2

To find the value of x in the given right triangle, we will use the cosine function. According to trigonometry, the cosine of an angle is equal to the adjacent side divided by the hypotenuse:

$\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$

In this case, the angle is $34^{\circ}$, the adjacent side is $x$ mm, and the hypotenuse is $178$ mm. Therefore, we can express this relationship as:

$\cos(34^{\circ}) = \frac{x}{178}$

To find x, we rearrange this equation:

$x = 178 \times \cos(34^{\circ})$

Using a calculator, we find that:

$\cos(34^{\circ}) \approx 0.829$

Thus, substituting this back, we get:

$x \approx 178 \times 0.829 \approx 147.6 \text{ mm}$

Finally, rounding to one decimal place, we have:

$x \approx 147.6 \text{ mm}$