A hill is inclined at 18 degrees to the horizontal. If the base of the hill is at sea level, find my height above sea level if i walk 1.2 km up the hill
0.3090
To find your height above sea level after walking up the hill, we can use trigonometry.
The given angle of inclination is 18 degrees, and the distance you walked up the hill is 1.2 km.
Let's consider a right-angled triangle with the base as the distance you walked up the hill (1.2 km) and the height as the unknown value we want to find (your height above sea level).
We can use the trigonometric function tangent (tan) to solve for the height. The tangent of an angle is equal to the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.
So, let's calculate the height using the tangent function:
tan(θ) = opposite/adjacent
tan(18°) = height/1.2 km
Rearranging the equation to solve for the height:
height = tan(18°) * 1.2 km
Now, let's calculate the height:
Using a calculator or a trigonometric table, we can find that tan(18°) is approximately 0.3249.
height = 0.3249 * 1.2 km
height ≈ 0.3899 km
Therefore, your height above sea level after walking 1.2 km up the hill is approximately 0.3899 km.
To solve this problem, we will use trigonometry. First, let's draw a diagram to better understand the situation:
/|
/ |
h / | side opposite to the angle
/ |
/θ |
-------- <-- hill
distance
In this diagram, θ is the angle of inclination, h represents your height above sea level, and "distance" is the distance you walk up the hill.
We know that the angle of inclination is 18 degrees, and the distance you walk up the hill is 1.2 km. We need to find the height above sea level, which is represented by "h".
To find "h," we need to use trigonometric ratios. Specifically, we will use the tangent ratio, which relates the side opposite to the angle (h) and the side adjacent to the angle (distance).
The tangent of an angle (θ) is equal to the opposite side (h) divided by the adjacent side (distance).
In this case, the tangent of 18 degrees is:
tan(18 degrees) = h / 1.2 km
Now, let's solve for "h" using this equation:
h = tan(18 degrees) * 1.2 km
To solve this mathematically, start by calculating the value of tan(18 degrees) using a calculator. Then multiply that value by 1.2 km to get the value of "h".
After calculating it, the value of "h" represents your height above sea level.
height/walking distance= sin 18
solve for height