Question

applying the law of cosines to surveying
bob is standing 25 feet from a lamppost that is to his left and 30 feet from a lamppost that is to his right. the distance between the two lampposts is 20 feet. what is the measure of the angle formed from the line from each lamppost to bob? approximate to the nearest degree.

1. $20^{2}=25^{2}+30^{2}-2(25)(30)\cos(a)$
2. $400 = 625 + 900 -(1500)\cos(a)$
3. $400 = 1525 -(1500)\cos(a)$
4. $-1125 = -(1500)\cos(a)$

______ degrees

Explanation:

Step1: Isolate cos(A) term

Divide both sides by -1500:
$\frac{-1125}{-1500} = \cos(A)$

Step2: Simplify the fraction

$\cos(A) = 0.75$

Step3: Find inverse cosine

Calculate $\arccos(0.75)$:
$A = \arccos(0.75)$

Step4: Compute and round value

$A \approx 41.41^\circ$, rounded to nearest degree.

Answer:

41 degrees