from a second-storey window directly across the street. the angle of elevation of the top of an office building is 67 degre 30 mins. and the angle of depression of the base 18 degre 20 mins. if the building are 38 meter apart. wat is the height of the building ??
review your basic trig functions. You will see that the height is
38tan67°30' + 38tan18°20'
To calculate the height of the building, we can use trigonometric ratios and the given angles of elevation and depression.
Let's consider the triangle formed by the second-story window, the top of the office building, and the base of the office building.
We know that the angle of elevation is 67 degrees 30 minutes and the angle of depression is 18 degrees 20 minutes.
First, let's convert the angles to decimal degrees for easier calculations:
Angle of elevation = 67 degrees + 30 minutes = 67.5 degrees
Angle of depression = 18 degrees + 20 minutes = 18.3333 degrees
Now, let's label the triangle:
T
|\
| \
| \
| \
h | \ x
| \
|______\
B W
T = Top of the office building
B = Base of the office building
W = Second-story window
h = Height of the office building
x = Distance from the window to the base of the building
In the triangle, we have two right angles at W and B.
Using tangent, we can write the following equation:
tan(angle of elevation) = h / x
Rearranging the equation, we get:
h = x * tan(angle of elevation)
Using the given information, we have:
angle of elevation = 67.5 degrees
x = 38 meters
Substituting the values into the formula, we get:
h = 38 * tan(67.5 degrees)
Calculating the value using a calculator:
h ≈ 90.73 meters
Therefore, the height of the office building is approximately 90.73 meters.
To find the height of the building, we can use trigonometric concepts and the given angles of elevation and depression. Here's how you can solve the problem:
Step 1: Visualize the scenario
Imagine a triangle formed by the second-story window, the top of the office building, and the base of the building. The distance between the window and the base of the building is given as 38 meters.
Step 2: Identify the angles
The angle of elevation is the angle from the second-story window to the top of the building, which is 67 degrees 30 minutes. The angle of depression is the angle from the second-story window to the base of the building, which is 18 degrees 20 minutes.
Step 3: Set up the trigonometric equation
We'll use the tangent function for both the angle of elevation and the angle of depression. The tangent of an angle is equal to the ratio of the opposite side to the adjacent side.
For the angle of elevation:
tan(67 degrees 30 minutes) = height of the building / distance from the window to the base
For the angle of depression:
tan(18 degrees 20 minutes) = height of the building / distance from the window to the base
Step 4: Convert angles to decimal form
Before using the trigonometric functions, convert the angles to decimal form for easier calculations. To convert minutes to degrees, divide the number of minutes by 60.
67 degrees 30 minutes = 67 + 30/60 = 67.5 degrees
18 degrees 20 minutes = 18 + 20/60 = 18.33 degrees
Step 5: Solve the equation
Let's plug in the values into the trigonometric equations:
For the angle of elevation:
tan(67.5 degrees) = height of the building / 38 meters
For the angle of depression:
tan(18.33 degrees) = height of the building / 38 meters
Step 6: Calculate the height of the building
Using a calculator or the tangent function, solve for the height of the building in each equation:
For the angle of elevation:
height of the building = tan(67.5 degrees) * 38 meters
For the angle of depression:
height of the building = tan(18.33 degrees) * 38 meters
Step 7: Calculate the final answer
Add the values obtained from the two equations to find the height of the building:
height of the building = height from angle of elevation + height from angle of depression
This will give you the final height of the building.