h t t p : / / i m g 4 0 . i m a g e s h a c k . u s / c o n t e n t . p h p ? p a g e = d o n e& l = i m g 4 0 / 1 4 8 / a s d a s d y e . j p g & v i a = m u p l o a d

(def of tan theta = a^-1 o)a = o
opposite = adjacent tan theta

written with respect to the first angle

opposite = (adjacent 1 + adjacent 2) tan theta one

were adjacent 1 is the 50 feet

written for the second angle

opposite = adjacent 2 tan theta two

set them equal to each other

(adjacent 1 + adjacent 2) tan theta one = adjacent 2 tan theta two

distripute

adjacent 1 tan theta one + adjacent 2 tan theta one = adjacent 2 tan theta two

subtract from both sides

adjacent 1 tan theta one = adjacent 2 tan theta two - adjacent 2 tan theta one

factor or whatever

adjacent 1 tan theta one = adjacent 2 (tan theta two - tan theta one)

muliply by inverse to solve for adjacent 2

(adjacent 1 tan theta one = adjacent 2 (tan theta two - tan theta one)) ((tan theta two - tan theta one)^-1

adjacent two = (tan theta two - tan theta one)^-1 adjacent 1 tan theta one

plug and chug for adjacent two

adjacent two = (tan 32 degrees - tan 40 degrees)^-1 (50 ft) tan theta 40 degrees

I got negative 195.8 feet?

See:

http://img40.imageshack.us/i/asdasdye.jpg/

that would be the image i put up...

i don\'t understand???

If you look at the figure, you will see that θ1 should be smaller than θ2, but you have labelled θ1=40, and θ2=32.

Perhaps the two values have been inverted and perhaps that is the source of your problem.
Could you please check and let us know?

Yes, I translated the link so that other people could see your image without having to go through the hassle I had to.

hmmmm ok i\'ll try and see what i get thanks

high school Goraul vaishali

To answer the question, "I got negative 195.8 feet?", we can check your calculations step by step.

1. You mentioned the formula for the opposite side in terms of the adjacent side and the tangent of an angle: opposite = adjacent * tan(theta).
2. You defined the first angle as theta one.
3. According to your input, opposite = (adjacent1 + adjacent2) * tan(theta one).
4. You assigned a value of 50 feet to adjacent1.
5. For the second angle, you wrote: opposite = adjacent2 * tan(theta two).
6. You set both equations equal to each other: (adjacent1 + adjacent2) * tan(theta one) = adjacent2 * tan(theta two).
7. You then distributed the tan(theta one) to both adjacent terms: adjacent1 * tan(theta one) + adjacent2 * tan(theta one) = adjacent2 * tan(theta two).
8. Subtracting adjacent2 * tan(theta one) from both sides, you obtained: adjacent1 * tan(theta one) = adjacent2 * (tan(theta two) - tan(theta one)).
9. To solve for adjacent2, you multiplied both sides by the inverse of (tan(theta two) - tan(theta one)): adjacent2 = (tan(theta two) - tan(theta one))^(-1) * adjacent1 * tan(theta one).
10. Finally, you substituted the given values: adjacent2 = (tan(32 degrees) - tan(40 degrees))^(-1) * 50 ft * tan(40 degrees).

Now, let's calculate the result:
- Using a calculator, evaluate the subtraction inside the parentheses: (tan(32 degrees) - tan(40 degrees)) ≈ -0.522.
- Raise that value to the power of -1: (-0.522)^(-1) ≈ -1.912.
- Multiply this by 50 ft and by tan(40 degrees): (-1.912) * 50 ft * tan(40 degrees) ≈ -144.628 ft.

Therefore, the correct answer is approximately -144.628 feet, not -195.8 feet.