Question

From Times Square in New York City, you can see Central Park and the Empire State Building. The approximate distance from Times Square to Central Park is 2 miles, Central Park to the Empire State Building is 1.3 miles, and Empire State Building to Times Square is 0.9 miles. What is the approximate angle to the other two landmarks from the Empire State Building? 20.205° 29.926° 114.624° 129.868°

Answer 1

`\text{129.868}\degree`

Step-by-step explanation:

Here, we want to get the approximate angle to the other landmarks

To get this, we need a diagram that properly represents the information

We have this as follows:

To get the value of the marked angle, we can use cosine rule since we have all the sides

We have it that:

`\begin{gathered} e^2=c^2+t^2\text{ -2ct CosE} \\ 2^2=0.9^2+1.3^2\text{ -2(0.9)(1.3) cos E} \\ 1.5\text{ = }-2.34\text{ cos E} \\ m\angle E\text{ = }\cos ^(-1)(-(1.5)/(2.34)) \\ \\ m\angle E\text{ = 129.868}\degree \end{gathered}`