 Consider the following situation. Dirichlet attempts to measure the height of a flagpole, which you can see illustrated here in our diagram. But unfortunately, she can't measure the distance between herself and the flagpole directly because there's some type of fence that's between her and the flagpole. So the flagpole might be on private property or restricted area. So she can't actually get to the flagpole and measure the distance out and then calculate the angle of elevation. So instead, what she's going to do is the following. She's still going to measure the angle of elevation from some fixed point to the top of the flagpole. And that angle of elevation turns out to be 61.7 degrees. Then she's going to turn 90 degrees from her current point and she's going to walk 25 feet along perhaps like a sidewalk that's on the side of the fence there. And then she's going to make another angle measurement which that angle measurement turns out to be 54.5 degrees at some point B. So we have B right here. We have point A right there. And so using this information, how could she calculate the height of the flagpole? Well, why is the fence such a big deal here? Well, if we call the distance from the flagpole to Deirdre's original measurement, let's call that distance X right here. This gives us a right triangle here where the angle is given as 61.7 degrees. The distance at the bottom here at A is X. And then let's say that the height of the flagpole is equal to H. So if we use the tangent ratio, we're going to get that tangent of A is equal to H over X clearing the denominators. We get H is equal to X times tangent of A which is good news if she knew the distance between her angle measure and the flagpole but she doesn't because of that fence. So that's why she walked along the sidewalk to get a different measurement. Let's look at this second triangle going on right here. So if we look at this other triangle, it's a right triangle itself, what we know is we have this angle B which it equals 54.5 degrees. We have a right angle. We know this distance here is 25 and then we know this distance over here is X. It's the same X in play right here. And so if we use the tangent ratio in that situation, we're going to get that X over 25 is equal to tangent of B and therefore X is equal to 25 times tangent of B. So if we make this substitution in here for X, we didn't get that H is equal to 25 times tangent of A times tangent of B. So even though there was a fence obstructing her, she still was able to measure the height of this flagpole assuming she knows these angle measurements. So the exact answer for H will be 25 times tangent of A which was 61.7 degrees. We're going to times that also by tangent of B. B remember was 54.5 degrees like so. And so put these in your calculator. Make sure your calculator is in degree mode when you do that calculation. And if we round to the nearest 0.1 foot, we see that 25 times tangent of 61.7 degrees times tangent of 54.5 degrees would turn out to be 65.1 feet, which would be the approximate height of the flagpole.