In widening a highway, it is necessary for a construction crew to cut into the bank along a highway. The present angle of elevation of the straight slope of the bank is 24°, and the new angle is to be 38.5°, leaving the top of the slope at its present position. If the slope of the present bank is 210 ft. long, how far horizontally into the bank must they dig?

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lublana lublana · Answer 1 · 2020-03-31T08:12:51+02:00

Answer:

84.4 m

Step-by-step explanation:

We are given that

[tex]\theta=24^{\circ}[/tex]

The new angle,[tex]\theta'=38.5^{\circ}[/tex]

Slop of the present bank=210 ft

We have to find the horizontal distance into the bank must they dig.

[tex]Sin\theta=\frac{Perpendicular\;distance}{Hypotenuse}[/tex]

[tex]sin24=\frac{h}{210}[/tex]

[tex]h=210sin24=85.4 m[/tex]

[tex]cos\theta=\frac{base}{Hypotenuse}[/tex]

[tex]cos24=\frac{x}{210}[/tex]

[tex]x=210cos24=191.8 m[/tex]

[tex]tan\theta'=\frac{perpendicular\;distance}{Base}=\frac{h}{x'}[/tex]

[tex]tan38.5=\frac{85.4}{x'}[/tex]

[tex]x'=\frac{85.4}{tan38.5}=107.4 m[/tex]

The horizontal distance they have to dug=191.8-107.4=84.4 m