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

label the top of the building as P and its bottom as Q

look at triangle PAB
angle A = 21°
angle ABP = 180-32 = 148° , then
angle APB = 11°

using the sine law you can find PB
then in the right-angled triangle PBQ
BQ/BP = cos32
BQ = BPcos32 = ....

add 100 and BQ

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

To find the distance between point A and the foot of the building, we can use trigonometry and the concept of tangent.

Let's call the height of the building "h" and the distance between point A and the building "x."

From point A, the angle of elevation to the top of the building is 21 degrees. This means that the tangent of 21 degrees is equal to the opposite side (h) divided by the adjacent side (x). Mathematically, this can be written as:

tan(21 degrees) = h / x

Similarly, from point B, the angle of elevation to the top of the building is 32 degrees. Using the same logic, we have:

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

We can rearrange these equations to solve for x. First, isolate h in both equations:

h = x * tan(21 degrees)

h = (x + 100) * tan(32 degrees)

Since the height of the building, h, is the same in both equations, we can set these two equations equal to each other:

x * tan(21 degrees) = (x + 100) * tan(32 degrees)

Now, let's solve this equation to find the value of x:

x * tan(21 degrees) = x * tan(32 degrees) + 100 * tan(32 degrees)

x * tan(21 degrees) - x * tan(32 degrees) = 100 * tan(32 degrees)

x * (tan(21 degrees) - tan(32 degrees)) = 100 * tan(32 degrees)

x = (100 * tan(32 degrees)) / (tan(21 degrees) - tan(32 degrees))

Using a scientific calculator, evaluate the tangent functions and calculate x:

x ≈ 110.88 meters

Therefore, point A is approximately 110.88 meters away from the building.