Question

in the given diagram, calculate x correct to 2 decimal places. 25 42° x

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, the cosine of an angle is defined as $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here, $\theta = 42^{\circ}$, the adjacent side is $x$, and the hypotenuse is $25$. So, $\cos42^{\circ}=\frac{x}{25}$.

Step2: Solve for $x$

We can rewrite the equation from Step 1 as $x = 25\times\cos42^{\circ}$.
We know that $\cos42^{\circ}\approx0.7431$ (using a calculator).
Then $x = 25\times0.7431$.
$x=18.5775$.

Answer:

$18.58$