Question

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?

Answer 1

Answer:

84.4 m

Step-by-step explanation:

We are given that

$\theta=24^{\circ}$

The new angle,$\theta'=38.5^{\circ}$

Slop of the present bank=210 ft

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

$Sin\theta=\frac{Perpendicular\;distance}{Hypotenuse}$

$sin24=\frac{h}{210}$

$h=210sin24=85.4 m$

$cos\theta=\frac{base}{Hypotenuse}$

$cos24=\frac{x}{210}$

$x=210cos24=191.8 m$

$tan\theta'=\frac{perpendicular\;distance}{Base}=\frac{h}{x'}$

$tan38.5=\frac{85.4}{x'}$

$x'=\frac{85.4}{tan38.5}=107.4 m$

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