# Math Help - Trig Word Problem... Help!

1. ## Trig Word Problem... Help!

To find the length of a swamp, a surveyor stands at a point P, 85 yd from one end of the swamp and 90 yd from the other end. He measures the angle between the lines of sight to be 92o. Find the length of the swamp.

Can someone show or explain to me how to set a problem like this up? Thanks!

2. Originally Posted by KarlosK
To find the length of a swamp, a surveyor stands at a point P, 85 yd from one end of the swamp and 90 yd from the other end. He measures the angle between the lines of sight to be 92o. Find the length of the swamp.

Can someone show or explain to me how to set a problem like this up? Thanks!
Hi KarlosK,

This looks like a classic case for the cosine rule.

$c^2=a^2+b^2-2ab\cos c$

$c^2=85^2+90^2-(85)(90)\cos 91$

You need to find c.

3. Masters thanks for taking the time to help me. I programmed the equation in with the numbers you had given me and it came out to 453659.9, which can not be correct??

I went to Irregular Triangle Calculator

and entered what I thought were the correct numbers into the triangle equation. I came out with an answer that the swamp is about 26.63 yards. Does that seem correct?

4. @masters

That is an awesome image.

How did you generate it?

It looks as if you used 'paint' for the black/white part, but
HOW did you overlay the information in red?

KarlosK
The 92 degree angle is close to 90 degrees.
Roughly you have a right triangle.
The hypotenuse is the unknown length.

$
85^2 + 90^2 = 15325
$

$
\sqrt{15325} = 123.8
$

That lets you know what you should expect for the answer.
& further (this is just my thinking)
$
sin(2degs)*(85+90) = 6.1
$

thus: what I am looking for is
"between"
(123.8 - 6.1) = 117.7
& (123.8 + 6.1) = 129.9

I know that ANY answer outside that range is wrong.

Then use the cosine rule as explained by masters to get the correct answer.

5. Originally Posted by KarlosK
Masters thanks for taking the time to help me. I programmed the equation in with the numbers you had given me and it came out to 453659.9, which can not be correct??

I went to Irregular Triangle Calculator

and entered what I thought were the correct numbers into the triangle equation. I came out with an answer that the swamp is about 26.63 yards. Does that seem correct?
Hi KarlosK,

If you use the cosine rule as I laid out you should arrive at approximately 125.9 yds.

If you use your handy dandy calculator you found, you enter 255 ft for side A, 270 ft for side B and 92 for angle C. The result is in feet: 377.79712 ft.

You have to divide that by 3 to convert to yards.

The answers are the same: 125.93237 yds.

Aidan: This is just a crude drawing using Microsoft Paint.

6. Thanks both of you. Very helpful, and honestly much better teacher than my online professor.