Question

find the missing side. round to the nearest ten
1)
10
70°
x

Explanation:

Step1: Identify trigonometric ratio

We have a right triangle, with the side opposite the 70° angle equal to 10, and \(x\) is the hypotenuse. Use sine:
$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$

Step2: Substitute known values

Plug in $\theta=70^\circ$, opposite=10, hypotenuse=$x$:
$\sin(70^\circ) = \frac{10}{x}$

Step3: Solve for \(x\)

Rearrange to isolate \(x\):
$x = \frac{10}{\sin(70^\circ)}$
Calculate $\sin(70^\circ) \approx 0.9397$, so:
$x \approx \frac{10}{0.9397} \approx 10.64$

Step4: Round to nearest tenth

Round 10.64 to one decimal place:
$x \approx 10.6$

Answer:

10.6