Question

applying the law of cosinesbob 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)$$square$ degrees

Explanation:

Step1: Isolate $\cos(A)$

Divide both sides by $-1500$:
$\frac{-1125}{-1500} = \cos(A)$
$\cos(A) = 0.75$

Step2: Calculate angle $A$

Use inverse cosine function:
$A = \cos^{-1}(0.75)$

Step3: Approximate to nearest degree

$A \approx 41^\circ$

Answer:

41 degrees