A window in a building is 15.0m above the ground. From this window the angle of elevation to the top of the second building is 32degrees and the angle of depression to the bottom of the second building is 17degrees. What is the height of the second building? -diagram needed please or an explanation of it.
Tan 17 = h1/d.
Tan 17 = 15/d, d = 49.1 m. = Distance between the buildings.
Tan32 = h2/d.
Tan32 = h2/49.1, h2 = 30.7 m. = ht. from window of 1st bldg. to top of 2nd bldg.
h = h1+h2 = 15 + 30.7 = 45.7 m. = ht. of 2nd bldg.
A diagram of the problem:
1. Draw a rectangle with the longest sides hor.
2. Draw a hor. line through the ver. sides to form two rectangles.
3. Label the ver. sides of the lower rectangle h1(15m) and the ver. sides of the top rectangle h2.
4. Draw a diagonal from the upper left corner of the lower rectangle. The angle of depression formed is 17o.
5. Draw a diagonal from lower left corner of the top rectangle. The angle of elevation formed is 32o.
To determine the height of the second building, we can use trigonometry and the information given in the problem. Let's break down the problem step by step.
Step 1: Draw a diagram
To better understand the problem, let's draw a simple diagram:
|\
| \
| \
| \
| \
| \
Second Building h | |\ |
| | \ d|
| | \ |
| | \ |
| | \ |
| | \
|_____|______\
Window b
In the diagram, "h" represents the height of the second building, "b" represents the distance between the window and the base of the second building, and "d" represents the distance between the window and the top of the second building.
Step 2: Identify the given information
From the problem, we know that the window is 15.0m above the ground, and we have two angles of elevation and depression. The angle of elevation to the top of the second building is 32 degrees, and the angle of depression to the bottom of the second building is 17 degrees.
Step 3: Use trigonometry to find the height of the second building
Using trigonometry, we can create two right triangles based on the given angles.
In the first right triangle:
The opposite side is h (height of the second building).
The adjacent side is b (distance between the window and the base of the second building).
Using the tangent function: tan(32°) = opposite/adjacent, we can write:
tan(32°) = h/b
In the second right triangle:
The opposite side is h (height of the second building).
The adjacent side is d (distance between the window and the top of the second building).
Using the tangent function: tan(17°) = opposite/adjacent, we can write:
tan(17°) = h/d
Step 4: Solve the equations
Now, we have two equations with two variables (h and b). We can solve them simultaneously to find the values.
Equation 1: tan(32°) = h/b
Equation 2: tan(17°) = h/d
Rearranging Equation 1:
b = h / tan(32°)
Substituting the value of b into Equation 2:
tan(17°) = h / (h / tan(32°))
Simplifying Equation 2:
tan(17°) = tan(32°) * h / h
Canceling out the h terms:
tan(17°) = tan(32°)
Since tan(17°) is not equal to tan(32°), it means there is no solution.
Therefore, based on the given information, it is not possible to determine the height of the second building with the given angles of elevation and depression.