swatuna21
Answered

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A sign on a roadway at the top of a mountain indicates that for the next 4 miles, the grade is 10.5°. Find the change in elevation over that distance for a car descending the mountain. Round to the nearest hundredth.

Sagot :

facundo3141592

the change in elevation is -0.73 miles (the negative sign is because the new elevation is smaller than the initial one).

How to find the change in elevation?

To do this, we can think on the situation as a right triangle, where the hypotenuse is 4 miles, the angle that we look at measures 10.5°, and the change in elevation (let's call it x) will be the opposite cathetus to that angle.

Then we can use the relation:

Sin(a) = (opposite cathetus)/(hypotenuse)

Replacing what we know, we get:

sin(10.5°) = x/4mi

x = sin(10.5°)*4mi = 0.73mi

So the change in elevation is -0.73 miles (the negative sign is because the new elevation is smaller than the initial one).

If you want to learn more about right triangles:

https://brainly.com/question/2217700

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