Question

A park was created from an old city block. There is a path that begins as a sidewalk outside and goes diagonally through the park. If the length of the short end of the block is 72 yards, how long is the path inside the park?

Answer 1

Looking at the image, there is a angle of 150°, which is an external angle of the upper right triangle in the figure.

The internal angle relative to this external angle measures 30° (they are a linear pair, therefore they are supplementary angles).

In order to find the measure of the path inside the park, let's use the sine relation of the angle 30°.

The sine is equal to the length of the opposite leg to the angle over the length of the hypotenuse.

So we have:

`\begin{gathered} \sin30°=(72)/(x)\\ \\ (1)/(2)=(72)/(x)\\ \\ x=72\cdot2\\ \\ x=144\text{ yd} \end{gathered}`

Therefore the path has a length of 144 yards.