Through what angle does the observer see the pole?

Question

One end of a 9.3 foot pole is 13.6 feet from an observer's eyes, and the other end is 17.4 feet from the observer's eyes. Through what angle does the observer see the pole?

Answer 1

sin θ = 9.3 / 17.4

sin θ ≈ 0.534482759

sin^-1 0.534482759 ≈ θ

32.3° ≈ θ

Answer 2

The Law of Cosines should help solve this problem. 

 

a²=b²+c²-2bccosA where A is the angle opposite side a. The pole is side a, with lines of sight from the observer's eyes to either end of the pole represented by b and c. Check to ensure that these numbers do indeed form a triangle (the sum of any two sides is greater than the 3rd).

 

So, cosA = (13.6² + 17.4² - 9.3²)/2x13.6x17.4

 

A = arc cos (the value of the expression above); my calculator gave me 32 degrees (rounded off).