Problem

A ramp rises \(3~\text{ft}\) at a \(6°\) angle with level ground. Use the diagram to identify the relevant sides, write a trigonometric equation, and find ramp length \(L\) to \(\text{two}~\text{decimal}~\text{places}\).

A right-triangle ramp rises 3 feet at a 6-degree ground angle with unknown ramp length L on the hypotenuse; the trigonometric equation and result are withheld.

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Fix the right-triangle geometry before calculating: label the known side and unknown side relative to the given angle. Use the trigonometric ratio containing exactly those two roles, solve the equation symbolically, and evaluate in degree mode. Keep calculator precision until the final rounding, then check that a shallow angle produces a suitably long hypotenuse.

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The 3-foot rise is opposite 6 degrees and L is the hypotenuse, so sin(6 degrees)=3/L and L=3/sin(6 degrees)=28.70 feet.

Round sin(6 degrees) to 0.1 before solving, so L=3/0.1=30.00 feet.

Use sin(6)=3/L in radian mode, so L=3/sin(6 radians)=-10.74 feet.

Treat the 3-foot rise as adjacent to 6 degrees, so cos(6 degrees)=3/L and L=3/cos(6 degrees)=3.02 feet.

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A ramp rises \(3~\text{ft}\) at a \(6°\) angle with level ground. Use the diagram to identify the relevant sides, write a trigonometric equation, and find ramp length \(L\) to \(\text{two}~\text{decimal}~\text{places}\).

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