george is in a hot air balloon that is 125 metres high. the angle of elevation from a house below, to the balloon is 18 degrees. how far is george from the house
it would be 125 divided by sin 18 which is aproximently 404.5
To find the distance between George in the hot air balloon and the house, we can use trigonometry. We are given the height of the balloon (125 meters) and the angle of elevation (18 degrees). Let's denote the distance between George and the house as 'x.'
From the given information, we can set up the following trigonometric relationship:
tan(18 degrees) = opposite/adjacent
The opposite side is the height of the balloon (125 meters), and the adjacent side is the distance between George and the house (x). Therefore, we can rewrite the equation as:
tan(18 degrees) = 125/x
Now we can solve for x by rearranging the equation:
x = 125 / tan(18 degrees)
Using a calculator, we can find that the value of tan(18 degrees) is approximately 0.3249. Substituting this value into the equation:
x = 125 / 0.3249
Calculating the division, we find:
x ≈ 384.48 meters
Therefore, George is approximately 384.48 meters away from the house.
To find the distance between George and the house, we can use trigonometry. Let's assume that George is directly above the house.
In a right-angled triangle, with the house at the base, the height of the hot air balloon (125 meters) is the opposite side, and the distance from the house to George is the adjacent side. The angle of elevation (18 degrees) is the angle between the opposite side and the hypotenuse.
We can use the tangent function to find the length of the adjacent side (distance from the house to George):
tan(angle) = opposite / adjacent
tan(18 degrees) = 125 meters / distance from the house to George
To solve for the distance, we rearrange the equation:
distance from the house to George = 125 meters / tan(18 degrees)
Calculating this using a calculator:
distance from the house to George ≈ 369.52 meters
Therefore, George is approximately 369.52 meters away from the house.
let that distance be h , (the hypotenuse)
I see it as
sin18° = 125/h
h = 125/sin18
= ...