Question

From the entrance, most people will go straight to the roller coaster or straight to the tower. The distance from the entrance to the roller coaster is 461m, and the distance from the entrance to the tower is 707 m. If the paths to these two attractions are separated by a 41o angle, how far apart are the roller coaster and the tower?

Answer 1

The given situation can be illustrated as follow:

In order to determine the distance x between the roller coaster and the tower. Use the law of cosines, as follow:

`x^2=(461)^2+(707)^2-2(461)(707)\cos 41`

By simplifying the previous expression, you obtain:

`\begin{gathered} x^2=220409.5413 \\ x=\sqrt[]{220409.5413} \\ x\approx469.5 \end{gathered}`

Hence, the distance between the tower and the roller coaester is approximately 469.5m