Answer:
<h3>First, recall the three basic right triangle trigonometry ratios.</h3>
<h3>sin(θ)=opposite/hypotenuse</h3><h3>cos(θ)= adjacent/hypotenuse</h3><h3>tan(θ)= opposite/adjacent</h3><h3>Theta (θ) represents the angle. The angle (other than the right angle) is 70 degrees.</h3>
<h3>We are also given 2 sides: 10 and x.</h3>
<h3>10 is the hypotenuse, because it is opposite the right angle.</h3><h3>x is opposite the 70 degree angle.</h3><h3>Since we have the opposite and hypotenuse, we must use sine.</h3>
<h3>sin (\Theta)= \frac{opposite}{hypotenuse}}</h3>
<h3>The angle is 70 degrees, the opposite is x, and the hypotenuse is 10.</h3>
<h3>sin(70)=\frac{x}{10}sin(70)= </h3><h3>10</h3><h3>x</h3>
<h3>We are solving for x. We must isolate x on one side of the equation.</h3>
<h3>Currently, x is being divided by 10. To "undo" the division, we must perform the inverse operation, which is multiplication. Multiply both sides of the equation by 10.</h3>
<h3>10*sin(70)=\frac{x}{10}*1010∗sin(70)= </h3><h3>10</h3><h3>x</h3>
<h3> ∗10</h3>
<h3>10*sin(70)=x10∗sin(70)=x</h3>
<h3>10*0.939692621=x10∗0.939692621=x</h3>
<h3>9.39692621=x9.39692621=x</h3>
<h3>Round to the nearest tenth. The 9 in the hundredth place tells us to round the 3 up to a 4.</h3>
<h3>9.4 \approx x9.4≈x</h3>
<h3>x is about 9.4</h3>