I need an expert to figure out the length of a line.

[evanesq]

Geometry was never my thing and there is just no way I can figure this out.

I'm building a shed in my yard, where the front wall will be higher than the rear wall to allow rain to wash down the roof to the back.

The front wall is 8 feet high, and the roof will descend at an angle of 15 degrees.

The depth of the shed is 8 feet.

How tall is the rear wall?

I really appreciate your help

 

[Deleted member 4993]

Geometry was never my thing and there is just no way I can figure this out.

I'm building a shed in my yard, where the front wall will be higher than the rear wall to allow rain to wash down the roof to the back.

The front wall is 8 feet high, and the roof will descend at an angle of 15 degrees.

The depth of the shed is 8 feet.

How tall is the rear wall?

I really appreciate your help

If

the height of the front wall = F

the height of the back wall = B

Neglecting the thickness of the wall:

(F - B) = 8 * tan(15°)

 

[evanesq]

If

the height of the front wall = F

the height of the back wall = B

Neglecting the thickness of the wall:

(F - B) = 8 * tan(15°)

So I looked up a tangent calculator, and it tells me that the tangent of 15 degrees is .26794919.

I multiply that by 8, and I get 2.143595

So that would mean (8 - B) = 2.143595

Subtract 8 from both sides, and resolve the negative on both sides and the answer is 5.85641 ...?

Seems right.. is that correct?

 

[djdisko]

Geometry was never my thing and there is just no way I can figure this out.

I'm building a shed in my yard, where the front wall will be higher than the rear wall to allow rain to wash down the roof to the back.

The front wall is 8 feet high, and the roof will descend at an angle of 15 degrees.

The depth of the shed is 8 feet.

How tall is the rear wall?

I really appreciate your help

so the front wall is 8ft and higher than the back, so its x ft higher.
This means that the back wall is 8 - x ft high. So we need to find x
As shown in my professional diagram, you need to use tan (o/a).
The depth of the shed is the opposite, so 8/x = tan15
Rearrange it for x and you get 8/tan15.
Take x off 8 and you have your answer

 

[Steven G]

So I looked up a tangent calculator, and it tells me that the tangent of 15 degrees is .26794919.

I multiply that by 8, and I get 2.143595

So that would mean (8 - B) = 2.143595

Subtract 8 from both sides, and resolve the negative on both sides and the answer is 5.85641 ...?

Seems right.. is that correct?

If you have a little more than 2 and then subtract 8, I doubt you will have more than 5. Think this way, if you have $2.14 in your bank account and somehow you convince your bank to let you take out $8 do you really believe that your balance is $5.85???? Redo that calculation.