Question

Jacob is looking up at an object Jacob points one arm at the object and the other arm at Kevin . The angle formed by his outstretched arms measures 45 degrees Kevin is also looking up at the object he points one arm at the object and the other arm at Jacob the angle formed by his outstretched arms measures 30 degrees the distance between the two men is 80 feet which of the following best represents the distance between Jacob and the object
A: 55.7 ft
B:53.2 feet
C:41.4
D:48.9

Answer 1

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,

$\frac{sin O}{JK}=\frac{sin 30^{\circ}}{JO}$

$\implies JO sin O = JK sin 30^{\circ}$

$\implies JO = \frac{JK sin 30^{\circ}}{sin O}$

By substituting the values,

$JO=\frac{80\times sin 30^{\circ}}{sin 105^{\circ}}$

$=41.4110472164\approx 41.4$

Hence, the distance between Jacob and the object is approximately 41.4 feet.

Option C is correct.

Answer 2

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In this case Choice C would be the right answer