Question

solve for x. round to the nearest tenth, if necessary. 1 22° 16 k x j

Explanation:

Step1: Identify trigonometric relation

In right - triangle IJK, we know the hypotenuse $IK = 16$ and we want to find the side opposite to the angle $\angle I=22^{\circ}$. We use the sine function. The sine of an angle in a right - triangle is defined as $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. So, $\sin(22^{\circ})=\frac{x}{16}$.

Step2: Solve for $x$

Multiply both sides of the equation $\sin(22^{\circ})=\frac{x}{16}$ by 16. We get $x = 16\times\sin(22^{\circ})$.
We know that $\sin(22^{\circ})\approx0.3746$. Then $x = 16\times0.3746=5.9936$.

Step3: Round the result

Rounding $5.9936$ to the nearest tenth gives $x\approx6.0$.

Answer:

$x\approx6.0$