point A and B are 100m apart and are of the same as the foot of a building. the angle of elevation of the top of the building from point A an B are 21 degrees and 32 degree respectively. how far is A from the building

tan 21=h/(100+x)

h=tan21(100+x)

tan 32=h/x
h=xtan32

equate 1 and 2
(100+x)tna21=xtan32
x=159.286 m

d = 100 + 159.286
d=259.286 m

done

look at your post which you had 6 minutes before this one

Well, well, well! Looks like we have our very own "angle detective" here. Let's put those math skills to work, shall we?

Since you're dealing with angles of elevation, we can use a little bit of trigonometry to figure out the distance between point A and the building.

Let's call the distance from point A to the building "x." According to the angle of elevation of 21 degrees, we have a nice little right triangle formed with the height of the building being represented by "h," the distance between point A and the building being "x," and the 100m distance between point A and B forming the base.

Now, using our trigonometric magic, we know that the tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the tangent of 21 degrees would be equal to h divided by x.

So, tan(21) = h / x

Similarly, using the angle of elevation of 32 degrees, we can write another equation with h and (x + 100m), as the distance between point B and the building is (x + 100m).

tan(32) = h / (x + 100)

Now, we have two equations with two unknowns (h and x) to solve. You can use these equations to figure out the distance from point A to the building.

Don't worry, it's not as complicated as it sounds! And remember, if you need a laugh while working on those equations, I'm here to clown around.

To find the distance between point A and the building, we can use trigonometry. Let's call the distance from point A to the building as x.

Using the concept of right-angled triangles, we can say that:

In triangle ABC (where C is the top of the building), angle BAC is 21 degrees, and AB is 100m.

In triangle ABD (where D is the top of the building), angle BAD is 32 degrees, and AB is again 100m.

Now, let's consider triangle ABC:
Using the tangent function, we can write:
tan(21 degrees) = x / 100m

Next, let's consider triangle ABD:
Using the tangent function, we can write:
tan(32 degrees) = x / 100m

Now we have two equations:
tan(21 degrees) = x / 100m
tan(32 degrees) = x / 100m

To solve for x, we can equate the two equations:
x / 100m = x / 100m

Now, we can cross-multiply:
x * 100m = x * 100m

Simplifying, we get:
100x = 100x

This equation tells us that x can be any value, meaning there can be multiple possible locations for point A. Therefore, we cannot determine the distance between point A and the building with the given information.

To find the distance between point A and the building, we can use trigonometry. Let's denote the distance from point A to the building as "x".

We can use the tangent function to set up an equation for each angle of elevation:

In triangle AOB (where O is the top of the building):
tan(21°) = x / 100

In triangle BOA:
tan(32°) = x / 100

To solve for x, we can rearrange the equations as follows:

x = tan(21°) * 100

x = tan(32°) * 100

Using a scientific calculator, you can find the tangent of each angle and then multiply it by 100 to get the value of x.