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A road has an incline of 10°. To the nearest foot, find the increase in altitude of a car after driving 4,000 feet along the road. A) 695 ft B) 705 ft C) 3,939 ft D) 4,062 ft

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MrGumby
A. 

You can get this by creating a right triangle with a opposite side of x and the hypotenuse of 4000. Then find the altitude using Sin(10) = x/4000. Solve for x. 
boffeemadrid

Answer:

(A) 695ft

Step-by-step explanation:

Given: A road has an incline of 10°.

To find: The increase in altitude of a car after driving 4,000 feet along the road.

Solution: It is given that A road has an incline of 10°, thus using the trigonometry, we have

[tex]\frac{AB}{AC}=sin10^{\circ}[/tex]

Substituting the given values, we get

[tex]\frac{x}{4000}=sin10^{\circ}[/tex]

[tex]\frac{x}{4000}=0.174[/tex]

[tex]x=4000(0.174)[/tex]

[tex]x=694.5ft[/tex]

[tex]x[/tex]≈[tex]695ft[/tex]

Thus, the increase in altitude of a car after driving 4,000 feet along the road is 695 feet.

Hence, option A is correct.

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