Question

Chef Part A ROOFING A roofer rests a ladder at a height of 12 feet against a building so that the base of the ladder is x feet from the bottom of the side of the building, forming a 71.6° angle with the ladder and ground. Find the distance from the bottom of the ladder to the side of the building. a. Write an equation that can be used to find the distance from the bottom of the ladder to the side of the building. Part B b. How far is the bottom of the ladder from the side of the building? Round to the nearest tenth if necessary.​

Answer 1

• A: tan(71.6°) = (12 ft)/BG
• 4.0 ft

Explanation:

You want an equation and its solution for the distance from a building to the base of a ladder leaning at an angle of 71.6° to a point 12 ft up the side of the building.

Part A. Equation

The tangent function gives the relation between the legs of a right triangle:

Tan = Opposite/Adjacent

In the attached diagram, that tells us ...

tan(71.6°) = BL/BG

The equation that can be used to find the distance BG is ...

tan(71.6°) = (12 ft)/BG

Part B. Distance

The solution to the equation is ...

BG = (12 ft)/tan(71.6°) ≈ 4.0 ft

The bottom of the ladder is about 4.0 feet from the side of the building.

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