Thread: Trig angle problem

A woman on an island wishes to reach point R on a straight shore on the mainland from a point P on the island. The point P is 9km from the shore and 15km from the point R. If the woman rows a boat at a rate of 3 km/h to a point Q on land, then walks the rest of the way at a rate of 5km/h, express the total time it takes the woman to reach point R as a function of the indicated angle

So this is what I've gotten so far

sin(theta) = 9/PQ so PQ = 9/sin(theta).


Call the point at the right angle S.


RS = sqrt(15^2 + 9^2) = sqrt(225 + 81) = sqrt(306) = 17.5


9/QS = tan(theta)


QS = 9/tan(theta)


QR = 17.5 - 9/tan(theta)
PQ = 9/sin(theta)


she travels 3km/h on PQ and 5 on QR. So it's PQ/3 + QR/5.

Is there a way to find out the lengths of PQ or QR or is what I have the answer?

use s=vt to find t.find time taken to travel from P to Q and then add it to the time taken to travel from Q to R. You will get the answer in terms of theta. The lengths PQ and QR can only be found if the angle is given.

Hello, OVechkin8!

A woman on an island wishes to reach point on a straight shore
on the mainland from a point on the island.
The point is 9 km from the shore and 15k m from the point
If the woman rows a boat at a rate of 3 km/h to a point on land,
then walks the rest of the way at a rate of 5 km/h,
express the total time it takes to reach point as a function of the indicated angle

Code:

      : - - - - - 12  - - - - :
      S   x   Q      12-x     R
      o - - - o - - - - - - - o
      |      *             *
      |     *           *
      |    *         *
    9 |   *       * 15
      |  *     *
      |θ*   *
      |* *
      o
      P

Let

In right triangle
Pythagorus says: .

Let: , then


In right triangle

She rows km at 3 km/hr.

. . This will take her: . hours.


In right triangle
Hence: .

She walks km at 5 km/hr.

. . This will take her: . hours.


Therefore, her total time is: . hours.