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A surveyor measures the lengths of the sides of a triangular plot of land. What is the measure of the angle of the triangular plot at which the surveyor stands? Approximate to the nearest degree.

A. [tex] \cos^{-1}(0.75) = 41^{\circ} [/tex]
B. [tex] \cos^{-1}(0.125) = 83^{\circ} [/tex]
C. [tex] \cos^{-1}(0.563) = 56^{\circ} [/tex]
D. [tex] \cos^{-1}(0.15) = 89^{\circ} [/tex]

Sagot :

GinnyAnswer
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].
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