Answer:
20.8
Step-by-step explanation:
To solve for [tex]\sf x [/tex] using trigonometry, we can use the sine function because we have the opposite side(x) and the hypotenuse (100) given, and we are dealing with a right triangle.
Set up the equation using sine:
The sine of an angle in a right triangle is defined as the ratio of the length of the opposite side to the length of the hypotenuse.
[tex]\sf \sin(\theta) = \dfrac{\textsf{opposite}}{\textsf{hypotenuse}} [/tex]
Here:
- [tex]\sf \theta = 12^\circ [/tex],
- the opposite side(x) and
- the hypotenuse is 100.
Substitute the value:
[tex]\sf \sin(12^\circ) = \dfrac{x}{100} [/tex]
Therefore, Ratio is:
[tex]\sf \sin(12^\circ) = \dfrac{x}{100} [/tex]
Now, solve for x.
We can rearrange the equation to solve for [tex]\sf x [/tex].
[tex]\sf x = 100 \times \sin(12^\circ) [/tex]
Calculate [tex]\sf x [/tex]:
Use a calculator to find the value of [tex]\sf \sin(12^\circ) [/tex] and then calculate [tex]\sf x [/tex].
[tex] sin(12^\circ =0.2079116908177 [/tex]
Therefore,
[tex]\sf x = 100 \times 0.2079116908177 [/tex]
[tex]\sf x = 20.79116908177 [/tex]
Round the answer:
Finally, round [tex]\sf x [/tex] to the nearest tenths place.
[tex]\sf x \approx \boxed{20.8} [/tex]
Explanation:
To solve for x, we used the sine ratio which relates the opposite side and the hypotenuse of a right triangle.
By substituting the known values (opposite = x), hypotenuse = 100) into the sine function, we set up an equation and solved for x by multiplying the hypotenuse (100) by the sine of the given angle (12°). The calculated value of x is then rounded to the nearest tenths place to get the final answer is 20.8.
