To determine the measure of the angle at which the surveyor stands, we will analyze the given cosine values and their corresponding angles. Here's the step-by-step solution:
1. Identify the cosine values and corresponding angles:
- [tex]\(\cos^{-1}(0.75) = 41^{\circ}\)[/tex]
- [tex]\(\cos^{-1}(0.125) = 83^{\circ}\)[/tex]
- [tex]\(\cos^{-1}(0.563) = 56^{\circ}\)[/tex]
- [tex]\(\cos^{-1}(0.15) = 89^{\circ}\)[/tex]
2. Determine which angle corresponds to a cosine value of 0.75:
- From the list, we note that [tex]\(\cos^{-1}(0.75) = 41^{\circ}\)[/tex].
3. Conclusion:
- Therefore, the measure of the angle at which the surveyor stands is [tex]\(41^{\circ}\)[/tex].
Thus, the angle at which the surveyor stands is [tex]\(41^{\circ}\)[/tex].
