Answer:
[tex]\boxed {\boxed {\sf x \approx 3.7}}[/tex]
Step-by-step explanation:
Since we are given a right triangle, we can use the trigonometric ratios.
- sin(θ)=opposite/hypotenuse
- cos(θ)= adjacent/hypotenuse
- tan(θ)=opposite/adjacent
We have the angle 24 and the sides 9 and x. 9 is the hypotenuse because it's opposite the right angle. x is the opposite, because it as across from the 24 degree angle. So, we have:
Therefore, we must use sine.
[tex]sin(24)= \frac{x}{9}[/tex]
We are trying to solve for the value of x, so we must isolate the variable. x is being divided by 9. The inverse of division is multiplication. Multiply both sides by 9.
[tex]9*sin(24)= \frac{x}{9}*9[/tex]
[tex]9*sin(24)=x[/tex]
[tex]9*0.406736643=x[/tex]
[tex]3.66062979=x[/tex]
Round to the nearest tenth. The 6 in the hundredth place tells us to round the 6 to a 7.
[tex]3.7 \approx x[/tex]
x is approximately 3.7
