Question

A rectangular park had a dirt path across its diagonal that was 100 yards long. The diagonal and the long side of the park formed an angle thatmeasured 40°.A person walked along the sidewalks outside the park, from the start to the end of the path, as shown by the arrows.ENDSTART100 yardsWhich expression shows the distance that he walked?200cos 40 153 yards100cos 40 + 100sin 40 141 yards100cot 40' 119 yards100tan 40+ 100tan 50 203 yards

Answer 1

Trigonometric ratios for given angle (40º) in a right triangle:

`\begin{gathered} sin40º=(opposite)/(hypotenuse) \\ \\ cos40º=(adjacent)/(hypotenuse) \end{gathered}`

The person walked the distance x+y

`\begin{gathered} sin40º=(y)/(100) \\ \\ y=100sin40º \\ \\ cos40º=(x)/(100) \\ \\ x=100cos40º \\ \\ x+y=100sin40º+100cos40º \\ x+y=140.88 \end{gathered}`

Then, the distance that walked the person is:

100cos40+100sin40=141 yards