the windshield on an automobile is inclined 42.5 degrees with respect to the horizontal. assuming that the windshield is flat and rectangular, what is its area if it is 1.50m wide and the bottom is 0.48m in front of the top?
0.977
To find the area of the windshield, you can break it down into a triangle and a rectangle.
1. Start by visualizing the windshield as a flat, rectangular shape. Since it is inclined at an angle of 42.5 degrees with respect to the horizontal, make sure to consider this angle when calculating the area.
2. Identify the two sides of the windshield. The width of the windshield, given as 1.50m, represents the bottom side. The vertical height of the windshield is the difference in distance between the bottom and top points (0.48m).
3. From the given dimensions, you can calculate the vertical side of the triangle formed by the windshield. Use the basic trigonometric function sine to find this dimension:
- sin(angle) = opposite/hypotenuse
- sin(42.5 degrees) = vertical side/width of windshield
- vertical side = sin(42.5 degrees) * 1.50m
4. Calculate the area of the triangle using the formula for the area of a triangle:
- Area of triangle = 0.5 * base * height
- Area of triangle = 0.5 * 1.50m * (vertical side)
5. Calculate the area of the rectangle by multiplying the width by the vertical height:
- Area of rectangle = width * height
- Area of rectangle = 1.50m * (vertical side)
6. Finally, add the areas of the triangle and rectangle to find the total area of the windshield.
Note: Ensure that all calculations are done in the same units (e.g., meters) for accurate results.
Using these steps, you should be able to calculate the area of the windshield.