Question

Hello! Need some help in between two answers, thank you!

Answer 1

To solve this, we need to use the Law of Cosines. GIven a triangle ABC:

The Law of Cosines tells us:

`a^2=b^2+c^2-2bc\cdot\cos(A)`

In the problem, we have 3 locations: Times Square (TS), Central Park (CP) and the Empire State Building (ESB). And we know the distances between them:

TS to CP = 2 miles

TS to ESB = 0.9 miles

CP to ESB = 1.3 miles

Let's make a diagram:

And using the Law of Cosines:

`1.3=0.9^2+2^2-2\cdot0.9\cdot2\cdot\cos(\theta)`

And solve:

`\begin{gathered} 1.3^2=0.81+4-3.6\cos(\theta) \\ . \\ 1.69=4.81-3.6\cos(\theta) \\ . \\ 3.6\cos(\theta)=4.81-1.69 \\ . \\ \cos(\theta)=(3.12)/(3.6)=(13)/(15) \\ . \\ \theta=\cos^(-1)((13)/(15))\approx29.92643 \end{gathered}`

Thus, the correct answer is the second option, 29.926º