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Building A and building B are 500 meters apart. There is no road between them, so to drive from building A to building B, it is necessary to first drive to building C and then to building B. About how much farther is it to drive than to walk directly from building A to building B? Round to the nearest whole number. A) 183 meters B) 250 meters C) 366 meters D) 683 meters

Respuesta :

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Answer:

Option A) 183 meters

Step-by-step explanation:

see the attached figure to better understand the problem

step 1

Find the distance BC

we know that

In the right triangle ABC

[tex]cos(60\°)=\frac{BC}{AB}[/tex] ----> adjacent side divided by the hypotenuse

Remember that

[tex]cos(60\°)=1/2[/tex]

substitute the values

[tex]1/2=\frac{a}{500}[/tex]

[tex]a=250\ m[/tex]

step 2

Find the distance AC

In the right triangle ABC

[tex]sin(60\°)=\frac{AC}{AB}[/tex] ----> opposite side divided by the hypotenuse

Remember that

[tex]sin(60\°)=\frac{\sqrt{3}}{2}[/tex]

substitute the values

[tex]\frac{\sqrt{3}}{2}=\frac{b}{500}[/tex]

[tex]b=250\sqrt{3}= 433\ m[/tex]

step 3

Find the distance AC+CB

[tex]433+250=683\ m[/tex]

Subtract the distance AB from 683 m

[tex]683-500=183\ m[/tex]

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Answer:

a)183

Step-by-step explanation:

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