Question

6.

Viola drives 170 m up a hill that makes an angle of 6° with the horizontal. Rounded to the nearest tenth of a meter, what horizontal distance has she covered?

169.1 m

17.8 m

1,617.4 m

171.5 m

Answer 1

(a) 169.1 m

Explanation:

The diagram shows you the distance (x) will be shorter than 170 m, but almost that length. The only reasonable answer choice is ...

169.1 m

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The relevant trig relation is ...

Cos = Adjacent/Hypotenuse

The leg of the right triangle adjacent to the marked angle is x, and the hypotenuse is 170 m. Putting these values into the equation, you have ...

cos(6°) = x/(170 m)

x = (170 m)cos(6°) ≈ (170 m)(0.994522) ≈ 169.069 m

The horizontal distance covered is about 169.1 meters.

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Additional comment

Expressed as a percentage, the slope of this hill is tan(6°) ≈ 10.5%. It would be considered to be a pretty steep hill for driving.