A road 1.6 km long rises 400 m. What is the angle of elevation of the road?
I don't known which numbers go to which sides. I can do the rest once I can label the triangle. Thanks!
In your right-angled triangle, the hypotenuse would be the 1.6 km road and its height would be the 400 m
The horizontal, or the "run", would be the side you have to find by Pythagoras.
Don't forget to change to either metres or km.
THATS WHY I COULDN'T GET THE RIGHT ANSWER! i didn't convert the meters! thank you
The rise is the vertical dimension y and the length of the road (1.6 km) is the hypotenuse of a right triangle-- tha actual distance covered.
On a map, the length of the road would be the x (horizontal) distance covered, but that is not what I think they mean by the "road length" here.
The angle of elevation is
sin^-1 0.4/1.6 = sin ^-1 0.25
= 14.48 degrees
yes that's the answer i got drwls thanks the m km messed me up =]
To label the triangle, we need to identify the sides and angles. Let's assume the road is represented by a straight line segment, where one end is at ground level and the other end is at a higher point. We can call the horizontal distance (the base of the triangle) as 'x' and the vertical distance (the height of the triangle) as 'y'. The road, being a straight line, represents the hypotenuse of the triangle.
Given that the road is 1.6 km long and rises 400 m, we have:
Base (x) = 1.6 km = 1600 m
Height (y) = 400 m
Hypotenuse (road) = 1.6 km
Now, we can use the trigonometric definition of the tangent function to find the angle of elevation. The tangent of an angle is equal to the ratio of the opposite side (y) to the adjacent side (x).
Using the formula:
tan(angle) = opposite/adjacent
In this case, we have:
tan(angle) = y/x
tan(angle) = 400/1600
Now, we can calculate the tangent of the angle:
tan(angle) = 0.25
Finally, to find the angle itself, we take the inverse tangent (arctan) of the tangent value:
angle = arctan(0.25)
Using a calculator or a trigonometric table, we find:
angle ≈ 14.03 degrees
Therefore, the angle of elevation of the road is approximately 14.03 degrees.