From point A,the angle of elevation to the top of a tall building is 20 degrees.On walking 80 m towards the building,the angle of elevation is now 23 degrees.How tall is the building?

stanley u are wrong the answer is 204.1m

Make a sketch, label the top of the building P and its bottom Q.

On the ground, label angle A = 20 and mark point B as 23 degrees
then angle ABP = 180-23 = 157 degrees
angle A = 20 and angle APB = 3 degrees
by the sine law
BP/sin20 = 80/sin3
BP = 80sin20/sin3
= ....

then in the right-angled triangle BPQ
sin 23 = PQ/BP

take over

Well, you know what they say about buildings – they're just like piñatas, except instead of candy, they're filled with mysteries! Let's solve this one together.

So, from point A, the angle of elevation to the top of the building is 20 degrees. When you walk 80 meters towards the building, the angle of elevation increases to 23 degrees.

Now, if we think about it, the change in angle of elevation is due to the fact that you're getting closer to the building. It's like when you stand in front of a mirror and close in on your reflection – it appears larger!

Using a bit of trigonometry, we can deduce that the height of the building can be found using the tangent function. We can set up the following equation:

tan(23 degrees) = (height of building) / (80 meters)

Now, we just need to solve for the height of the building. Are you ready for the big reveal?

Drumroll, please...

Based on my not-so-scientific calculations, the height of the building will be approximately (80 meters) * tan(23 degrees). So, get your calculator ready, and you'll have your answer!

Remember, though, this is just an estimate. It would be best to measure the building directly, just to be sure. But hey, at least now you have a solid starting point for your investigation!

To find the height of the building, we can use trigonometry. Let's start by labeling the given information.

Let the height of the building be 'h' meters.
The distance from point A to the building is 'x' meters.

From point A, the angle of elevation to the top of the building is 20 degrees. This means that we have a right triangle formed, with the height of the building as the opposite side and the distance 'x' as the adjacent side.

Using trigonometry, we can say:

tan(20 degrees) = h / x

Next, we have another right triangle formed when we move 80 meters towards the building. In this case, the distance from the new point (let's call it B) to the building is 'x - 80' meters. The angle of elevation is now 23 degrees.

Using trigonometry again, we can say:

tan(23 degrees) = h / (x - 80)

Now, we have two equations to solve simultaneously. Let's solve for 'h' in both equations.

From the first equation:
tan(20 degrees) = h / x

Multiplying both sides by x:
x * tan(20 degrees) = h

From the second equation:
tan(23 degrees) = h / (x - 80)

Multiplying both sides by (x - 80):
(x - 80) * tan(23 degrees) = h

Since both equations equal 'h', we can set them equal to each other:

x * tan(20 degrees) = (x - 80) * tan(23 degrees)

Now, we can solve for 'x'.

x * tan(20 degrees) = x * tan(23 degrees) - 80 * tan(23 degrees)

Divide both sides by tan(20 degrees):

x = (x * tan(23 degrees) - 80 * tan(23 degrees)) / tan(20 degrees)

Now, we can substitute this value of 'x' back into one of the original equations to find 'h':

h = x * tan(20 degrees)

Plug in the value of 'x':

h = [(x * tan(23 degrees) - 80 * tan(23 degrees)) / tan(20 degrees)] * tan(20 degrees)

Simplifying further:

h = (x * tan(23 degrees) - 80 * tan(23 degrees)) / tan(20 degrees)

Finally, plug in the values of the angles into the equation above using a calculator to get the height 'h' of the building.

h= 220.95m