# Thread: Extremely hard trigo prob: "Nathan is swimming across a river from A to B..."

1. ## Extremely hard trigo prob: "Nathan is swimming across a river from A to B..."

Nathan is swimming across a river from A to B. He iscurrently at N, having swum 30 m. If he was to changecourse and head directly for the opposite bank, he will savehimself 20 m of swimming. Given that the river is 50 m wide,how much further must Nathan swim to get to B?

2. Originally Posted by vedansh
Nathan is swimming across a river from A to B. He is currently at N, having swum 30 m. If he was to change course and head directly for the opposite bank, he will save himself 20 m of swimming. Given that the river is 50 m wide,how much further must Nathan swim to get to B?

Is the current in the river negligible?

Looks like points A and B are not directly opposite of each other.

3. ## Yes, the current is negligible. Here is a representational image

img 1.png
Originally Posted by Subhotosh Khan
Is the current in the river negligible?

Looks like points A and B are not directly opposite of each other.

4. Originally Posted by vedansh
Assuming the banks are parallel, we know that the angle at A formed by the lower bank and the line AB is equal to the angle at B formed by the upper bank and the line AB. We can add another vertical line, dropped from B to the lower bank (at a point we'll call "C"), which forms another right triangle. If we label his new landing point on the upper bank "L", we then have two similar right triangles, ABC and BNL.

We can label the distance from A to N as "a", the distance from N to B as "b", the distance from N to L as "n", and the segment BC as "50", which is given to us. We are also, though, given that "a" must equal 30, and that "n" must equal b - 20. So we can label our picture like this:

Code:
labels:

L           B
-------------*-----------*--
|        x /|
|        /  |
n = b - 20 |      /    |
|    /      |
|  /  b     |
*/          |
/N           |
/              |
a = 30  /                |
/                  | 50
/                    |
/ x                    |
-*-----------------------*--
A                       C
See what you can do with sine ratios for the base angles "x" of the two triangles....

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