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

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:

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:

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

step-by-step explanation:

the answer is 128

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240