To calculate [tex]\(\frac{20}{\cos 70^{\circ}}\)[/tex] and round the result to one decimal place, follow these steps:
1. Evaluate the Cosine: Start by calculating [tex]\(\cos 70^{\circ}\)[/tex]. The value of [tex]\(\cos\)[/tex] for [tex]\(70^{\circ}\)[/tex] is needed for the division.
2. Division: Once you have the value of [tex]\(\cos 70^{\circ}\)[/tex], divide 20 by this value. This will give you the exact value of the expression [tex]\(\frac{20}{\cos 70^{\circ}}\)[/tex].
3. Rounding: Finally, round the resultant value to one decimal place.
Now, let's break down these steps with the numerical values:
1. The value of [tex]\(\cos 70^{\circ}\)[/tex] is approximately [tex]\(0.3420\)[/tex].
2. To find [tex]\(\frac{20}{0.3420}\)[/tex], perform the division:
[tex]\[
\frac{20}{0.3420} \approx 58.47608800326173
\][/tex]
3. Round this value to one decimal place:
[tex]\[
58.47608800326173 \approx 58.5
\][/tex]
So, [tex]\(\frac{20}{\cos 70^{\circ}}\)[/tex] rounded to one decimal place is [tex]\(58.5\)[/tex].
