Question

what is the approximate value of x? round to the nearest tenth. 3.1 cm 3.9 cm 4.6 cm 5.4 cm

Explanation:

Step1: Use cosine function

We know that $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here $\theta = 50^{\circ}$, the adjacent side to the $50^{\circ}$ angle is $x$ and the hypotenuse is $6$ cm. So $\cos(50^{\circ})=\frac{x}{6}$.

Step2: Solve for $x$

Multiply both sides of the equation $\cos(50^{\circ})=\frac{x}{6}$ by $6$. We get $x = 6\times\cos(50^{\circ})$.
Using a calculator, $\cos(50^{\circ})\approx0.6428$, then $x=6\times0.6428 = 3.8568\approx3.9$ cm.

Answer:

$3.9$ cm