Question

A rectangular park has a dirt path across its diagonal that was 100 yards long. The diagonal and the long side of the park formed an angle that measures 40 degrees. A person walked along the sidewalks outside the park, from the start to the end of the path, as shown by the arrows.Which expression shows the distance that he walked?

Answer 1

We would find the values of x and y

Distance walked = x + y

From the right angle triangle,

x = adjacent side

y = opposite side

hypotenuse = 100

θ = 40

We would find x by applying the cosine trigonometric ratio which is expressed as

Cosθ = adjacent side/hypotenuse

Cos40 = x/100

x = 100Cos40 = 77

We would find y by applying the sine trigonometric ratio which is expressed as

Sinθ = opposite side/hypotenuse

Sin40 = y/100

y = 100Sin40 = 64.3

Distance = 100Cos40 + 100Sin40 = 141 yards