# Calculating the time of a Trip

• Nov 12th 2008, 07:09 AM
magentarita
Calculating the time of a Trip
Two oceanfront homes are located 8 miles apart on a straight stretch of beach, each a distance of 1 mile from the paved road that parallels the ocean. Sally can jog 8 miles per hour along the paved road but only 3 miles per hour in the sand on the beach. Because of a river directly between the two houses, it is necessary to jog in the sand to the road, continue on the road and then jog directly back in the sand to get from one house to the other. The time T to get from one housee to the other as a function of the angle theta is given by:

T(theta) = 1 + (3/[3 sin(theta)] - 1/[4 tan (theta)], where
0 < theta < (pi/2).

Calculate the time T for tan (theta) = (1/4)
• Nov 12th 2008, 07:52 AM
HallsofIvy
Quote:

Originally Posted by magentarita
Two oceanfront homes are located 8 miles apart on a straight stretch of beach, each a distance of 1 mile from the paved road that parallels the ocean. Sally can jog 8 miles per hour along the paved road but only 3 miles per hour in the sand on the beach. Because of a river directly between the two houses, it is necessary to jog in the sand to the road, continue on the road and then jog directly back in the sand to get from one house to the other. The time T to get from one housee to the other as a function of the angle theta is given by:

T(theta) = 1 + (3/[3 sin(theta)] - 1/[4 tan (theta)], where
0 < theta < (pi/2).

Calculate the time T for tan (theta) = (1/4)

If $\displaystyle tan(\theta)= 1/4$ you can think of this as a right triangle with "opposite side" of length 1 and "near side" of length 4. Use the Pythagorean theorem to determining the length of the hypotenuse. From that you can get $\displaystyle sin(\theta)$ and the rest is just arithmetic.
• Nov 12th 2008, 04:46 PM
magentarita
ok but........
Quote:

Originally Posted by HallsofIvy
If $\displaystyle tan(\theta)= 1/4$ you can think of this as a right triangle with "opposite side" of length 1 and "near side" of length 4. Use the Pythagorean theorem to determining the length of the hypotenuse. From that you can get $\displaystyle sin(\theta)$ and the rest is just arithmetic.

Can I plug (1/4) in the given function for tangent and sine and simplify?