From the roof of a building, the angle of elevation of the top of a taller building is 37 degrees. The angle of depression of the base of the building is 28 degrees. The buildings are 21 m a part. Determine the height of the taller building

tan 37 = htop/21

tan 28 = hlow /21

so
htop + hlow = 21(tan37+tan28)

To solve this problem, we can use trigonometric ratios. Let's label the height of the taller building as 'x' meters.

Step 1: Determine the height of the shorter building
Since the angle of depression from the roof of the building is 28 degrees, we can use the tangent function. Tan(28) = shorter building height / distance between buildings.
Tan(28) = shorter building height / 21 m

To find the height of the shorter building, we can rearrange the equation:
Shorter building height = 21 m * tan(28)
Shorter building height ≈ 10.8 m

Step 2: Determine the height of the taller building
Now, we can use the height of the shorter building and the angle of elevation to find the height of the taller building. Since the angle of elevation is 37 degrees, we can use the tangent function again. Tan(37) = taller building height / distance between buildings.
Tan(37) = taller building height / 21 m

To find the height of the taller building, we can rearrange the equation:
Taller building height = 21 m * tan(37)
Taller building height ≈ 15.5 m

Therefore, the height of the taller building is approximately 15.5 meters.

To find the height of the taller building, we can use trigonometry and set up a right triangle.

Let's call the height of the taller building "h", and the distance between the buildings "d", which in this case is 21 meters.

From the roof of the first building, we have an angle of elevation of 37 degrees to the top of the taller building. This means that the opposite side is "h" and the adjacent side is "d".

Let's first find the length of the adjacent side using the angle of depression. Since the angle of depression is 28 degrees to the base of the taller building, this means that the opposite side is "h" and the adjacent side is "d". However, we need the length of the adjacent side, so we'll use the complementary angle, which is 90 - 28 = 62 degrees.

Now, using trigonometry, we can set up the following equation:
tan(62) = d / h

Rearranging the equation, we get:
h = d / tan(62)

Substituting the value of "d" (21 meters) and calculating the tangent of 62 degrees, we can find the height of the taller building:

h = 21 / tan(62)

Calculating this using a calculator:
h ≈ 21 / 1.8807265

So, the height of the taller building is approximately 11.16 meters.