A certain mountain road is inclined 3.1° with respect to the horizon. what is the change in altitude of the car as a result of its traveling 2.90 km along the road?

[tex]Given:\\ \alpha =3.1^\circ\\l=2.90km\\\\Find:\\h=?\\\\Solution:\\\\h=l\sin\alpha \\\\h=2.90km\cdot \sin 3.1^\circ=2.90km\cdot 0.054=0,1566km=156.6m[/tex]

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hamzaahmeds hamzaahmeds · Answer 2 · 2022-02-22T11:48:51+01:00

This question involves the concept of trigonometric ratios and right-angled triangle.

The change in altitude of the car will be "156.8 m".

CHANGE IN ALTITUDE OF CAR

Assuming a right-angled triangle, the hypotenuse of the triangle will serve as the length of the road, while the perpendicular will serve as the change in altitude of the car. The angle of inclination here is given. The scenario is presented in the attached picture.

Now, we will use the trigonometric ratio of sine to find out the change in altitude:

[tex]Sin\ \theta =\frac{perpendicular}{hypotenuse}=\frac{\Delta h}{L}\\\\\Delta h = (Sin\ \theta)(L)[/tex]

where,

θ = angle of inclination = 3.1°
Δh = change in altitude = ?
L = Length of road = 2.9 km = 2900 m

Therefore,

Δh = (Sin 3.1°)(2900 m)

Δh = 156.8 m

Learn more about the trigonometric ratios here:

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