Question

catherine starts at point a and walks 50 feet in one direction. jeff also starts at point a and walks 30 feet. the angle between their paths is 35°. how far apart are catherine and jeff when they stop walking? 5 of 12 questions 30.7 ft 63.7 ft 80.0 ft 76.5 ft

Explanation:

Step1: Apply the Law of Cosines

The Law of Cosines formula is \(c^{2}=a^{2}+b^{2}-2ab\cos C\). Here, \(a = 50\), \(b=30\), and \(C = 35^{\circ}\).
Substitute the values into the formula: \(c^{2}=50^{2}+30^{2}-2\times50\times30\times\cos(35^{\circ})\).

Step2: Calculate each term

First, \(50^{2}=2500\), \(30^{2} = 900\).
\(\cos(35^{\circ})\approx0.8192\), and \(2\times50\times30\times0.8192=2457.6\).
Then \(c^{2}=2500 + 900-2457.6\).
\(c^{2}=2500+900 - 2457.6=942.4\).

Step3: Find \(c\)

Take the square root of \(c^{2}\), \(c=\sqrt{942.4}\approx30.7\).

Answer:

30.7 ft