A library wishes to build an access ramp for wheelchairs. The main entrance of the library is 8 ft. above sidewalk level. If the architect recommends a grade (angle of elevation) of 6°, how long must the access ramp be?​

About 76.5 ft.

Step-by-step explanation:

Draw a diagram of a right triangle.  The shorter leg represents the height of the main entrance of the library, which is 8 ft.  The longer leg won't matter in this case.  The hypotenuse is what we're trying to find, so mark it as x.  We know there's a 6° angle of elevation, so the 30° angle of the triangle will be 6° in this case.  Now we have to use trig.  Think of Soh Cah Toa.  The 6° is opposite from 8 and the hypotenuse is x.  So, the equation to find x would be:

sin (6°) = 8/x

Multiply both sides by x

sin (6°) * x = 8

Divide both sides by sin (6°)

x = 8/sin (6°)

When putting it into a calculator, your answer should be 76.534, which rounds to 76.5 ft.

answer: city needs 2.4 inches of rainfall more to match the record of 40 inches.

step-by-step explanation:

since we have given that

total annual rainfall a city record = 40 inches

this year, total rainfall recorded = 37.6 inches

number of inches of rainfall   is needed to match the record of 40 inches is given by

hence, city needs 2.4 inches of rainfall more to match the record of 40 inches.

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step-by-step explanation: