A sign on a roadway at the top of a mountain indicates that

A sign on a roadway at the top of a mountain indicates that for the next 4 miles the grade is 10.5^o. Find the change in elevation over that distance for a car descending the mountain.

Solution

solution

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The side opposite the angle 10.5 deg is the change in elevation: Let it be h.

The hypotenuse is 4 miles. So since the opposite and hypotenuse

are involved,

Use sine function: sin(10.5 ) = h/4

h = 4sin(10.5) = 0.73 miles is the change in elevation