A painter is placing a ladder to reach the third story window, which is 18 feet above the ground and makes an angle with the ground of 80°.


How far out from the building does the base of the ladder need to be positioned? Round your answer to the nearest tenth.

The base of the ladder needs to be positioned *______*
feet out from the building.

so whats the answer ?

tan 80 = 18/x

so

x = 18/tan 80

To find out how far out from the building the base of the ladder needs to be positioned, we can use trigonometry.

We can use the sine function, which relates the length of the side opposite an angle to the length of the hypotenuse. In this case, the hypotenuse is the ladder and the opposite side is the height of the third story window.

The formula for sine is: sin(angle) = opposite/hypotenuse

We can rewrite this as: opposite = sin(angle) * hypotenuse

In this case, the angle is 80° and the hypotenuse is the distance we want to find. Let's call it "x". The opposite side is the height of the window, which is 18 feet.

So, we have: sin(80°) = 18/x

To find "x", we need to isolate it on one side of the equation.

Multiply both sides of the equation by "x":

x * sin(80°) = 18

Divide both sides of the equation by sin(80°):

x = 18 / sin(80°)

Now, we can calculate the value of "x" using a calculator:

x ≈ 18 / sin(80°) ≈ 18 / 0.9848 ≈ 18.29

So, the base of the ladder needs to be positioned approximately 18.3 feet out from the building (rounded to the nearest tenth).

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