Question

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°
cos–1(0.125) = 83°
cos–1(0.15) = 89°

Answer 1

Answer: Second option is correct.

Step-by-step explanation:

Since we have given that

a = 300 m

b = 250 m

c = 200 m

We need to find the measure of angle i.e. A

As we know the "Law of Cosine rules ":

$\cos A=\frac{b^2+c^2-a^c}{2bc}\\\\\cos A=\frac{250^2+200^2-300^2}{2\times 250\times 200}\\\\\cos A=\frac{12500}{100000}\\\\\cos A=0.125\\\\A=\cos^{-1}(0.125)\\\\A=82.81^\circ\\\\A\approx 83^\circ$

Hence, Second option is correct.

Answer 2

The second one is correct