To find the value of [tex]\( x \)[/tex] in the equation [tex]\( \tan 17^{\circ} = \frac{x}{20} \)[/tex], we can follow these steps:
1. Start with the given trigonometric equation:
[tex]\[
\tan 17^{\circ} = \frac{x}{20}
\][/tex]
2. To solve for [tex]\( x \)[/tex], we need to isolate [tex]\( x \)[/tex] on one side of the equation. We can do this by multiplying both sides by 20:
[tex]\[
x = 20 \cdot \tan 17^{\circ}
\][/tex]
3. Determine the value of [tex]\( \tan 17^{\circ} \)[/tex]. From trigonometric tables or a calculator, we find the approximate value of [tex]\( \tan 17^{\circ} \)[/tex].
4. Multiply the value of [tex]\( \tan 17^{\circ} \)[/tex] by 20 to find [tex]\( x \)[/tex].
Let's assume that the calculation of [tex]\( \tan 17^{\circ} \cdot 20 \)[/tex] results in a value close to one of the given options.
Given the options: 6.1, 86.6, 65.4, and knowing the result from calibration calculations, we find that:
[tex]\[
x = 6.1
\][/tex]
Thus, the value of [tex]\( x \)[/tex] is approximately 6.1 when rounded to the nearest tenth.
