Question

two points a and b are on opposite sides of a building. a surveyor chooses a third point c 71 yd from b and 97 yd from a, with angle acb measuring 58.2°. how far apart are a and b (to the nearest yard)?
a. 112 yd
b. 103 yd
c. 94 yd
d. 85 yd

Explanation:

Step1: Apply the Law of Cosines

The Law of Cosines formula is \( c^{2}=a^{2}+b^{2}-2ab\cos C\). Let \(a = 97\), \(b = 71\), and \(C = 58.2^{\circ}\).

Step2: Substitute values into the formula

$$
LATEXBLOCK0
$$

We know that \(\cos(58.2^{\circ})\approx0.527\).

$$
LATEXBLOCK1
$$

Step3: Find \(AB\)

Take the square root of \(AB^{2}\), \(AB=\sqrt{7180.1}\approx85\)

Answer:

D. 85 yd