Question

6)
find the value of x in the right triangle with one acute angle of 67° and the hypotenuse length of 12

Explanation:

Step1: Identify trigonometric ratio

We use cosine: $\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$
Here, $\theta=67^\circ$, adjacent side $=x$, hypotenuse $=12$.

Step2: Rearrange to solve for $x$

$x = 12 \times \cos(67^\circ)$

Step3: Calculate the value

Using a calculator, $\cos(67^\circ) \approx 0.3907$
$x \approx 12 \times 0.3907$

Answer:

$x \approx 4.69$