The grade of a highway up a hill is 50%. How much change in horizontal distance is there if the vertical height of the hill is 175 feet?
sinA = 50%/100% = 0.50.
A = 30o.
tan30 = Y/X = 175/X
X = 175/tan30 = 303 Ft.
To determine the change in horizontal distance, we need to use the formula for the grade of a highway. The grade is defined as the ratio of the vertical height to the horizontal distance traveled. In this case, the grade is given as 50%, which means it is equal to 0.5 in decimal form.
To find the horizontal distance, we can rearrange the formula to solve for it:
Grade = vertical height / horizontal distance
Rearranging the formula:
Horizontal distance = vertical height / grade
Plugging in the given values:
Horizontal distance = 175 feet / 0.5
Calculating:
Horizontal distance = 350 feet
Therefore, the change in horizontal distance is 350 feet.