john is standing 100 metres away from a building.the angle of elevationto the top of the building is8 degrees .He now walks straight away from the building.When he stopes,the angle of elevation is only 1 degree and 48 seconds.How far away is now from the base of the building.
Note that at 100m distance, the height of the building, h, is given by
h/100 = tan(8 deg) = 0.1405
h = 14.05 m
Now, farther away, at distance d,
h/d = tan(1.8 deg)
d = 14.05/0.0314 = 447.5m
To find the distance John is now from the base of the building, we can use trigonometry. Let's break it down step by step:
1. First, let's label some points. Let A represent the base of the building, and let B represent John's starting position 100 meters away from the building. Now, let C represent John's new position after walking straight away from the building.
A
/|
/ |
100 / |
/ | x
/ |
B-----C
2. We need to find x, the distance from C to the base of the building. To do this, we can use the tangent function. The tangent of an angle is equal to the opposite side divided by the adjacent side.
tan(angle) = opposite / adjacent
In this case, the angle is 1 degree and 48 seconds. We need to convert this into decimal degrees, which we can do by dividing the seconds by 60 and adding it to the degrees:
1 degree + (48 seconds / 60 seconds per minute) = 1.8 degrees
tan(1.8 degrees) = x / 100 meters
3. Now, we can solve for x by rearranging the equation:
x = tan(1.8 degrees) * 100 meters
Using a scientific calculator or trigonometric table, we can find that tan(1.8 degrees) is approximately 0.03133.
x ≈ 0.03133 * 100 meters
4. Calculate x:
x ≈ 3.133 meters
So, John is now approximately 3.133 meters away from the base of the building.