Question

applying the law of cosines to surveying
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.
$\cos^{-1}(0.75) = 41\degree$
$\cos^{-1}(0.125) = 83\degree$
$\cos^{-1}(0.563) = 56\degree$
$\cos^{-1}(0.15) = 89\degree$

Explanation:

Step1: Recall the Law of Cosines formula

The Law of Cosines formula is \(c^{2}=a^{2}+b^{2}-2ab\cos C\), where \(a = 200\), \(b = 250\), \(c = 300\), and \(C\) is the angle we want to find.

Step2: Substitute the values into the formula

$$
LATEXBLOCK0
$$

Step3: Find the angle \(C\)

\(C=\cos^{-1}(0.125)\)

Answer:

\(\cos^{-1}(0.125) = 83^{\circ}\)