solve for $x$. round to the nearest tenth, if necessary.\nanswer attempt 1 out of 2\n$x = $
solve for $x$. round to the nearest tenth, if necessary.\nanswer attempt 1 out of 2\n$x = $
Answer
Explanation:
Step1: Identify trigonometric ratio
In right - triangle VWU, we know the hypotenuse (WU = 86) and we want to find the side opposite the angle (56^{\circ}), so we use the sine function. The sine of an angle (\theta) in a right - triangle is defined as (\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}). Here, (\theta = 56^{\circ}), the opposite side is (x) and the hypotenuse is (86). So, (\sin(56^{\circ})=\frac{x}{86}).
Step2: Solve for (x)
Multiply both sides of the equation (\sin(56^{\circ})=\frac{x}{86}) by (86) to isolate (x). We know that (\sin(56^{\circ})\approx0.829). Then (x = 86\times\sin(56^{\circ})). [x=86\times0.829 = 71.394]
Step3: Round to the nearest tenth
Rounding (71.394) to the nearest tenth gives (71.4).
Answer:
(71.4)