a hill slopes upward at an angle of 14 degrees with the horizontal ground.what height does the man reach when he has traveled 100m upward from the foot of the hill
h = 100*sin14 =
To get answer
To find the height the man reaches when he has traveled 100m upward from the foot of the hill, we need to use the trigonometric relationship between the angle of inclination and the height.
1. Identify the given values:
- Angle of inclination: 14 degrees
- Distance traveled upward: 100m
2. Determine which trigonometric function to use.
Since we are given the angle and the opposite side (height), we can use the tangent function.
3. Apply the tangent function:
tan(angle) = opposite/adjacent
tan(14 degrees) = height/100m
4. Solve for the height using algebra:
height = tan(14 degrees) * 100m
Now, we can calculate the height reached by the man.
To find the height the man reaches when he has traveled 100m upward from the foot of the hill, we can use trigonometry and the concept of right triangles.
First, let's visualize the situation. We have a hill that slopes upward at an angle of 14 degrees with respect to the horizontal ground. When the man travels upward from the foot of the hill, he forms a right triangle with the hill.
Let's label the sides of the right triangle:
1. The horizontal distance the man travels along the ground is the base of the triangle and can be represented as "A."
2. The vertical height the man reaches is the height of the triangle and can be represented as "B." This is what we want to find.
3. The hypotenuse of the triangle represents the distance the man travels along the slope of the hill, which is given as 100m.
To find the height "B," we will use trigonometry. Specifically, we'll use the tangent function (abbreviated as tan).
The tangent of an angle in a right triangle is equal to the length of the opposite side divided by the length of the adjacent side.
In this case, the tangent of the angle of 14 degrees is equal to the height "B" divided by the horizontal distance "A".
So, we can set up the equation as follows:
tan(14 degrees) = B / A
To solve for the height "B," we rearrange the equation:
B = A * tan(14 degrees)
Substituting the given value of 100m for "A," we have:
B = 100m * tan(14 degrees)
Using a scientific calculator, you can find the value of tan(14 degrees) and calculate the height "B."