Fred was measuring the height of a building. He stood standing at some distance from

the building and measured an angle of 38 degrees to the top of the building. He then
walked 100 feet further away from the building and measured an angle of 34 degrees to
the top.
How tall is the building?

I know I'm suppose to use tan

I got tan38=y/x from the first part of the information. I need help getting the second part

from the outer triangle

tan 34 = y/(x+100)
y = (x+100)tan 34

from your equation
y = xtan 38

so xtan 38 = (x+100)tan 34
xtan 38 = xtan 34 + 100tan 34
xtan 38 - xtan 34 = 100tan 34
x(tan 38 - tan 34) = 100tan 34
x = 100tan 34/(tan 38 - tan 34)

once you found x, you can find y using your first equation.

you should help me mines is kinda like that and i don't understand it

To find the height of the building, we can use the tangent function (tan). As you mentioned, you correctly set up the equation tan38 = y/x for the first part of the information, where y represents the height of the building and x represents the distance between Fred and the building.

Now let's calculate the height of the building using the second part of the information:

First, we need to find the value of x for the second measurement. Since Fred walked 100 feet further away from the building, we can add 100 to the original distance x.

So, the new distance, let's call it x2, can be calculated as:
x2 = x + 100

Next, let's use the new angle measurement of 34 degrees. We can set up the equation tan34 = y/x2:

tan34 = y/(x + 100)

Now we have two equations:

tan38 = y/x
tan34 = y/(x + 100)

We can solve this system of equations simultaneously to find the height of the building.

Here's the step-by-step process to solve it:

1. Rearrange the first equation to solve for y:
y = tan(38) * x

2. Substitute this expression for y in the second equation:
tan(34) = (tan(38) * x) / (x + 100)

3. Multiply both sides of the equation by (x + 100):
(x + 100) * tan(34) = tan(38) * x

4. Expand the left side of the equation:
x * tan(34) + 100 * tan(34) = tan(38) * x

5. Rearrange the terms to isolate the x variable on one side:
x * (tan(34) - tan(38)) = 100 * tan(34)

6. Divide both sides of the equation by (tan(34) - tan(38)):
x = (100 * tan(34)) / (tan(34) - tan(38))

Now that we have found the value of x, we can substitute it back into the first equation (y = tan(38) * x) to find y, which represents the height of the building.

So, the height of the building is y.