find the length of side ( x ) to the nearest tenth.\nanswer attempt 1 out of 2\n( x = ) \nsubmit answer

Explanation:

Step1: Identify triangle type and trigonometric ratio

This is a right - triangle. We know that in a right - triangle, (\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}). For the (30^{\circ}) angle, the opposite side is (\sqrt{10}) and the hypotenuse is (x). So (\sin(30^{\circ})=\frac{\sqrt{10}}{x})

Step2: Solve for (x)

We know that (\sin(30^{\circ})=\frac{1}{2}). So we have the equation (\frac{1}{2}=\frac{\sqrt{10}}{x}). Cross - multiplying gives us (x = 2\sqrt{10})

Step3: Calculate the numerical value

We know that (\sqrt{10}\approx3.1623). Then (x = 2\times3.1623 = 6.3246)

Step4: Round to the nearest tenth

Rounding (6.3246) to the nearest tenth gives us (6.3)

Answer:

(6.3)