The angle of elevation from a car to the top of an apartment building is 48 degrees. If the angle from another car that is 22 feet directly in front of the

first car is 64 degrees. How tall is the building?

To solve this problem, we can use trigonometry. Let's represent the height of the building as h.

From the first car, the angle of elevation to the top of the apartment building is 48 degrees. This means that the height is the opposite side of the angle. We can use the tangent function to calculate the height:

tangent(48) = h / distance

Where distance is the distance between the first car and the building. Since we don't have this distance, we need to find another way to determine the value of h.

From the second car, the angle of elevation to the top of the apartment building is 64 degrees. This time, the distance between the second car and the building is given as 22 feet. Again, we can use the tangent function to calculate the height:

tangent(64) = h / 22

Now, we have two equations:

1. tangent(48) = h / distance
2. tangent(64) = h / 22

We can rearrange equation 1 to solve for distance:

distance = h / tangent(48)

Substituting this value into equation 2:

tangent(64) = h / (h / tangent(48))

Simplifying the equation:

tangent(64) = tangent(48)

Now, we can solve for h:

h = tangent(64) * 22

Using a calculator:

h ≈ 32.45 feet

Therefore, the building is approximately 32.45 feet tall.

To find the height of the building, we can use basic trigonometry. Let's break down the problem into two triangles:

Triangle 1: First car and top of the building
Triangle 2: Second car, first car, and top of the building

In Triangle 1, the angle of elevation from the car to the top of the building is 48 degrees. We need to find the height of the building, which is the opposite side of the angle. Let's call it "h".

In Triangle 2, the angle formed by the two cars and the height of the building is 64 degrees. We know the distance between the cars is 22 feet. We can call the height of the building in this triangle "x".

Now, we can set up a proportion using the tangent function:

tangent(48 degrees) = h/x

tangent(64 degrees) = h/(x + 22)

To find the height of the building, we need to solve these two equations simultaneously.

First, we solve the equation tangent(48 degrees) = h/x for h:

h = x * tangent(48 degrees)

Next, we solve the equation tangent(64 degrees) = h/(x + 22) for h:

h = (x + 22) * tangent(64 degrees)

Since both expressions equal "h", we can set them equal to each other:

x * tangent(48 degrees) = (x + 22) * tangent(64 degrees)

Now, we can solve for "x":

x * tangent(48 degrees) = x * tangent(64 degrees) + 22 * tangent(64 degrees)

x * (tangent(48 degrees) - tangent(64 degrees)) = 22 * tangent(64 degrees)

x = (22 * tangent(64 degrees)) / (tangent(48 degrees) - tangent(64 degrees))

After calculating this expression, you will get the value of "x". This value represents the height of the building in Triangle 2.

draw a diagram

review your trig functions. You will see that the height h can be found using

h cot48 - h cot64 = 22