Question

the movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer.
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 that measured 30°.
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?
100cot30°≈173 yards
100cos30° + 100sin30°≈137 yards
100tan30° + 100tan60°≈231 yards
200tan30°≈115 yards

Explanation:

Step1: Find the length of \(x\)

Using the cosine function: \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here \(\theta = 30^{\circ}\) and hypotenuse \(= 100\). So \(x = 100\cos30^{\circ}\)

Step2: Find the length of \(y\)

Using the sine function: \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here \(\theta = 30^{\circ}\) and hypotenuse \(= 100\). So \(y = 100\sin30^{\circ}\)

Step3: Calculate the total distance walked

The total distance walked is \(x + y\). Substituting the values of \(x\) and \(y\) we get \(100\cos30^{\circ}+100\sin30^{\circ}\)

Answer:

\(100\cos30^{\circ}+100\sin30^{\circ}\approx137\) yards (the second option)