A railroad track rises 30 feet for every 400 feet of track. What is the measure of the angle of elevation of the track?

Question

A railroad track rises 30 feet for every 400 feet of track. What is the measure of the angle of elevation of the track?

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Maria 3 weeks 2022-01-03T08:40:04+00:00 1 Answer 0 views 0

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  1. Charlotte
    0
    2022-01-03T08:41:21+00:00

    Answer:

    Step-by-step explanation:

    Rising 30 feet for every 400 feet of track is not a very large angle of elevation.  We set this up as a right triangle to use right triangle trig to solve for the missing angle.  The height is 30 and the hypotenuse is 400.  The height is the side opposite the angle in question, and the hypotenuse is the hypotenuse! This is the sin ratio.  Setting up the ratio using our info:

    sin\theta=\frac{30}{400}

    When you are looking for a missing angle measure, as we are here, use the 2nd–>sin buttons to find the inverse of sin, which looks like this:

    sin^{-1}(

    Enter in the fraction 30/400 after the parenthesis and then hit enter to get the angle measure of 4.3 degrees.

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