Solution of problem:from the top of a building 55 ft high, the angle of elevation of the top of a vertical pole is 12 degrees, At the bottom of the building, the angle of elevation of the top of the pole is 24 degrees. find the height of the pole.

Hoping you made a diagram,

label the top of the pole P and its bottom Q
label the top of the building A and its bottom B

Now look at triangle PAB.
angle PAB = 90+12 = 102°
angle PBA = 90-24 = 66°
leaving angle APB = 12°

by the sine law:
PB/sin102 = 55/sin12
PB = 55sin102/sin12 , don't work it out yet

in right-angled triangle PQB
sin 24 = PQ/PB
PQ = PB sin24 = 55 sin102 sin24/sin12

now get your calculator out, and do it in one continuous operation.

105.25ft

Good job 👌👍✅🤔🤔

Well, let's start by looking at the situation. We have a building and a pole. The angle of elevation from the top of the building to the top of the pole is 12 degrees, and the angle of elevation from the bottom of the building to the top of the pole is 24 degrees.

Now, imagine if the pole was just the height of the building. The angle of elevation from the bottom of the building to the top of the pole would be the same as the angle of elevation from the top of the building to the top of the pole, right? But in this case, the angles are different.

So, that means that the pole must be taller than the building. In fact, the angle of elevation from the bottom of the building to the top of the pole is double the angle of elevation from the top of the building to the top of the pole.

Using this information, we can calculate the height of the pole. Let's call the height of the pole "x". We can set up the following equation:

tan(24 degrees) = (x + 55 ft)/55 ft

Solving for x, we get:

x = 55 ft * tan(24 degrees) - 55 ft

So, the height of the pole is approximately x = 23.41 ft.

I hope this helps, and that you don't find my humor too "pole"-arizing!

To find the height of the pole, we can use trigonometry. Let's break down the problem:

1. We have a building that is 55 ft high, and we need to find the height of the pole.
2. From the top of the building, the angle of elevation to the top of the pole is 12 degrees.
3. At the bottom of the building, the angle of elevation to the top of the pole is 24 degrees.

Let's denote the height of the pole as 'h'.

From the perspective of the top of the building, the angle of elevation of the top of the pole forms a right triangle with the base of the building and the height of the pole.

Using the tangent function, we can write:

tan(12°) = h / x

Where x represents the distance from the top of the building to the base of the building.

Similarly, from the bottom of the building, the angle of elevation to the top of the pole creates another right triangle. We can write:

tan(24°) = h / (x + 55)

Now, we have a system of two equations with two unknowns (h and x). We can solve this system to find the height, 'h', of the pole.

Since we have the values of the angles, we can plug the values into the equations and solve for 'h'.

So, the height of the pole can be found by solving the following system of equations:

tan(12°) = h / x

tan(24°) = h / (x + 55)

By solving these equations simultaneously, we can find the value of 'h' and thus determine the height of the pole.