A 14 foot long ramp is being built to access a front door in a house. The door is 5 feet above the ground. How far away from the base of the house must the ramp be placed? What angle will the ramp make with the ground?

The ramp must be placed 13.08 feet from the base of the house.

The angle the ramp will make with the ground is 20.92°.

Step-by-step explanation:

An illustrative diagram for the scenario is shown below.

In the diagram, d represents the distance of the door from the ground, r represents the length of the ramp and x represent the distance of the ramp from the base of the house.

To determine how far away from the base of the house the ramp must be placed, that is to determine x in the diagram.

The diagram is a right angle triangle and x can be determine using the Pythagorean theorem which states " the square of the hypotenuse equals sum of the squares of the other two sides"

In the diagram, the hypotenuse is r

∴ r² = d² + x²

r = 14 ft

d = 5 ft

∴ 14² = 5² + x²

196 = 25 + x²

Then, x² = 196 - 25

x² = 171

x = √171

x = 13.08

Hence, the ramp must be placed 13.08 feet from the base of the house.

Now, to determine what angle the ramp will make with the ground, that is θ in the diagram.

From the formula

Sinθ = Opposite / Hypotenuse

In the diagram, opposite = d = 5ft

and Hypotenuse = r = 14ft

∴ Sinθ = 5ft / 14ft

Sinθ = 0.3571

∴ θ = Sin⁻¹(0.3571)

θ = 20.92°

Hence, the angle the ramp will make with the ground is 20.92°.

answer set (b) 0.5, 3/4 80% is in order from least to greatest.  

step-by-step explanation:

in order to compare rational numbers to each other, it is much easier if they are in the same form.   typically, the best form in which to evaluate rational numbers is in decimals.   in order to convert a percent to a decimal, you would divide the given percentage by 100.   you can also accomplish the conversion by moving the decimal point over two places to the left.   for example, the decimal value of 80% is 80/100, or 0.8.   in order to convert a fraction to a decimal, you need to divide the numerator by the denominator.   for example, 3/4 is 0.75.   so, for choice (b) 0.5 3/4 (0.75), 80% (0.8) is the only choice in which the numbers are in order from least to greatest.