Question

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. 1 20² = 25² + 30² - 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: Start from the cosine - law equation

We have the equation \(-1125=-(1500)\cos(A)\). First, we can simplify it by canceling out the negative signs on both sides.
\(1125 = 1500\cos(A)\)

Step2: Solve for \(\cos(A)\)

Divide both sides of the equation \(1125 = 1500\cos(A)\) by 1500.
\(\cos(A)=\frac{1125}{1500}=\frac{3}{4}= 0.75\)

Step3: Find the angle \(A\)

Take the inverse - cosine of 0.75. \(A=\cos^{-1}(0.75)\)
Using a calculator, \(A\approx41.41^{\circ}\approx41^{\circ}\)

Answer:

41