The escalator rises 25° from the ground and a vertical distance of 42 feet. How much horizontal distance does the escalator cover? Round to the nearest tenth.

We need to use the trig function tangent. We have Ф=25°, opposite = 42 feet, and we need to find the adjacent side (horizontal distance).
tan(Ф) = opposite/adjacent
tan(25) = 42/adjacent
adjacent * tan(25) = 42
adjacent = 42/tan(25)
adjacent = 90.1

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ApusApus ApusApus · Answer 2 · 2019-07-06T12:07:43+02:00

Answer:

90.1 feet.

Step-by-step explanation:

Please find the attachment.

Let x represent horizontal distance.

We have been given that an escalator rises 25° from the ground and a vertical distance of 42 feet. We are asked to find horizontal distance covered by escalator.

We can see from our attachment that vertical distance is opposite side of 25 degree angle and horizontal distance is adjacent side.

We know that tangent relates opposite side of right triangle with adjacent.

[tex]\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}[/tex]

Upon substituting our given values, we will get:

[tex]\text{tan}(25^{\circ})=\frac{42}{x}[/tex]

[tex]x=\frac{42}{\text{tan}(25^{\circ})}[/tex]

[tex]x=\frac{42}{0.466307658155}[/tex]

[tex]x=90.06929\approx 90.1[/tex]

Therefore, the escalator covered a horizontal distance of 90.1 feet.