Find the time if walk directly from the parking lot to the house.

The time to get from the parking lot to the beach house can be expressed as a function of the angle is .

Observe the figure :

The house, the parking lot and the paved path makes an right angled triangle.

For which adjacent side = length of the paved path ft.

Opposite side = distance between the paved path and the house ft.

Here,

Hypotenuse = distance from house to parking lot.

Use Pythagorean theorem to find hypotenuse.

Pythagorean theorem : .

ft.

Time function is .

Quotient identity : .

.

Trigonometric ratio : .

.

Substitute the values of and in .

min.

The time if walk directly from the parking lot to the house is min.