A road has a grade (slope) of 15%. What is the angle of elevation of the road, to the nearest degree?
15% grade means that the tangent of the elevation angle is .15
To find the angle of elevation of the road, you can use the inverse tangent function (also known as the arctan function). But first, let's understand what a 15% grade means.
A road with a grade of 15% indicates that for every 100 units of horizontal distance traveled, the road rises (or falls) by 15 units vertically. In other words, the road has a slope of 15/100 or 0.15.
Now, to find the angle of elevation, we need to find the inverse tangent of the slope (0.15 in this case). The inverse tangent function (arctan) helps to find the angle whose tangent equals the given slope.
Using a scientific calculator or an online calculator, you can find the inverse tangent (arctan) of 0.15. When you calculate it, you will get approximately 8.53 degrees.
Therefore, the angle of elevation of the road to the nearest degree is 9 degrees.
To find the angle of elevation of the road, we need to use trigonometry. The angle of elevation is the angle formed between the horizontal ground and the road.
The grade of the road is given as 15%, which means that for every 100 units traveled horizontally, there is a vertical rise of 15 units.
To find the angle of elevation, we can use the tangent function. The tangent of an angle is equal to the ratio of the opposite side (vertical rise) to the adjacent side (horizontal distance).
In this case, the opposite side is the vertical rise (15 units) and the adjacent side is the horizontal distance (100 units).
So, the tangent of the angle of elevation is:
tan(angle) = opposite / adjacent
tan(angle) = 15 / 100
Using a calculator or a trigonometric table, we can find the angle whose tangent is equal to 15/100.
tan^-1(15/100) ≈ 8.54 degrees (rounded to two decimal places)
Therefore, the angle of elevation of the road is approximately 8.54 degrees to the nearest degree.