To find the value of [tex]\(32 \cos(85^\circ)\)[/tex] and round it to the nearest tenth, follow these steps:
1. Convert the angle from degrees to radians:
- The angle given is [tex]\(85^\circ\)[/tex].
- Degrees to radians conversion uses the formula:
[tex]\[
\text{radians} = \text{degrees} \times \frac{\pi}{180}
\][/tex]
- Therefore,
[tex]\[
85^\circ \times \frac{\pi}{180} \approx 1.4835 \text{ radians}
\][/tex]
2. Calculate the cosine of the angle in radians:
- Using [tex]\(1.4835\)[/tex] radians:
[tex]\[
\cos(1.4835) \approx 0.0872
\][/tex]
3. Multiply by 32:
- Now, multiply the cosine value by 32:
[tex]\[
32 \times 0.0872 \approx 2.789
\][/tex]
4. Round to the nearest tenth:
- The nearest tenth of 2.789 is 2.8.
So, the value of [tex]\(32 \cos(85^\circ)\)[/tex] rounded to the nearest tenth is [tex]\(2.8\)[/tex].
