Question

6 directions - find the measure of x (round to two decimal places, show all work):

Explanation:

Step1: Identify trigonometric relation

We know that $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here $\theta = 47^{\circ}$, the adjacent side to the angle is $x$ and the hypotenuse is 3. So $\cos(47^{\circ})=\frac{x}{3}$.

Step2: Solve for x

Multiply both sides of the equation $\cos(47^{\circ})=\frac{x}{3}$ by 3. We get $x = 3\times\cos(47^{\circ})$.
Since $\cos(47^{\circ})\approx0.681998$, then $x=3\times0.681998 = 2.045994$.

Step3: Round the result

Rounding $2.045994$ to two - decimal places, we get $x\approx2.05$.

Answer:

$2.05$