find the value of $x$.\n$x \\approx \\square$\n(round to the nearest tenth as needed.)
find the value of $x$.\n$x \\approx \\square$\n(round to the nearest tenth as needed.)
Answer
Explanation:
Step1: Identify the trigonometric ratio
In a right triangle, the sine of an angle is the ratio of the opposite side to the hypotenuse. $$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$$
Step2: Substitute the given values
Substitute $\theta = 32^{\circ}$, opposite side $= x$, and hypotenuse $= 21$ into the formula. $$\sin(32^{\circ}) = \frac{x}{21}$$
Step3: Solve for x
Multiply both sides by 21 to isolate $x$. $$x = 21 \cdot \sin(32^{\circ})$$
Step4: Calculate the numerical value
Use a calculator to find the value and round to the nearest tenth. $$x \approx 21 \cdot 0.5299 \approx 11.128$$
Answer:
$x \approx 11.1$