A car travel 120m along a straight road which is inclined at 8° to the horizontal. Calculate the vertical distance through which the car rides ?
Draw the triangle : )
The vertical distance is the other leg of the triangle (not the hypotenuse).
Use the tangent ratio (opp/hyp) to obtain the value of the vertical distance : )
h/120 = sin 8°
To calculate the vertical distance that the car rides, you can use trigonometry.
Given:
Distance traveled along the road (horizontal distance) = 120 meters.
Angle of inclination = 8 degrees.
You can use the formula:
Vertical distance = Horizontal distance * Tan(angle of inclination)
Substituting the values:
Vertical distance = 120 meters * Tan(8°)
Using a calculator to find the tangent of 8 degrees, we get approximately 14.05.
Therefore:
Vertical distance = 120 meters * 14.05
Vertical distance ≈ 1686 meters.
So, the car rides approximately 1686 meters vertically.
To calculate the vertical distance through which the car rides, we need to calculate the component of the distance traveled in the vertical direction.
Step 1: Identify the given information:
- Distance traveled along the road (horizontal distance) = 120m
- Angle of inclination with the horizontal = 8°
Step 2: Calculate the vertical component:
The vertical component is given by the formula: Vertical distance = Horizontal distance * sin(angle of inclination)
So, Vertical distance = 120m * sin(8°)
Now, we can calculate the vertical distance by substituting the values into the formula:
Vertical distance = 120m * sin(8°)
= 120m * 0.139
= 16.68m
Therefore, the vertical distance through which the car rides is approximately 16.68 meters.