From h a point A that is 10 meters abov level ground, the angle of elevation of the top a building is 42 degrees and the angle of depression of the base of the building is 8 degrees approximate the height of the building
Let the building height be Y
Let the horizontal distance to the building be h.
h tan 42 = a
h tan 8 = b
Y = a + b = h (tan42,+ tan 8)
For the value of h, use
h tan 8 = 10 m
To approximate the height of the building, we can use trigonometric ratios and the given angles of elevation and depression.
First, let's understand the situation:
- Angle of elevation: The angle formed between the horizontal line (level ground) and the line of sight from the point A to the top of the building.
- Angle of depression: The angle formed between the horizontal line (level ground) and the line of sight from the point A to the base of the building.
- Height of point A: 10 meters.
To find the height of the building, we need to determine the horizontal distance between point A and the base of the building. Since the angles are measured from the horizontal line (level ground), we can assume that the line connecting point A to the building's base is parallel to the ground.
Let's use the tangent function to find the horizontal distance:
tan(8 degrees) = height of A / horizontal distance to the base of the building
Rearranging the equation, we get:
horizontal distance = height of A / tan(8 degrees)
Now, let's find the vertical height of the building:
tan(42 degrees) = height of A + vertical height of the building / horizontal distance to the base of the building
Since we already know the height of point A and the horizontal distance, we can rearrange the equation to solve for the vertical height of the building:
vertical height of the building = tan(42 degrees) x horizontal distance - height of A
Substituting the value of the horizontal distance from the previous calculation:
vertical height of the building = tan(42 degrees) x (height of A / tan(8 degrees)) - height of A
Finally, let's substitute the given values:
height of A = 10 meters
tan(8 degrees) = 0.1405
tan(42 degrees) = 0.9004
Calculating the height of the building:
vertical height of the building = 0.9004 x (10 / 0.1405) - 10
Therefore, the approximate height of the building is approximately 50.8556 meters.