Answer:
C. 41.4 feet
Step-by-step explanation:
Let J represents the position Jacob, K represents the position of Kevin and O represents the position of the object,
Since, By making the diagram of the given situation,
We found,
There is a triangle OJK, in which,
JK = 80 feet,
∠J = 45°,
∠K = 30°,
∠J + ∠K + ∠O = 180° ⇒ 45° + 30° + ∠O = 180° ⇒ ∠O = 180° - 75° = 105°,
By the law of sine,
[tex]\frac{sin O}{JK}=\frac{sin 30^{\circ}}{JO}[/tex]
[tex]\implies JO sin O = JK sin 30^{\circ}[/tex]
[tex]\implies JO = \frac{JK sin 30^{\circ}}{sin O}[/tex]
By substituting the values,
[tex]JO=\frac{80\times sin 30^{\circ}}{sin 105^{\circ}}[/tex]
[tex]=41.4110472164\approx 41.4[/tex]
Hence, the distance between Jacob and the object is approximately 41.4 feet.
Option C is correct.
