Question

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

Answer 1

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

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

Remember that

$cos(60\°)=1/2$

substitute the values

$1/2=\frac{a}{500}$

$a=250\ m$

step 2

Find the distance AC

In the right triangle ABC

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

Remember that

$sin(60\°)=\frac{\sqrt{3}}{2}$

substitute the values

$\frac{\sqrt{3}}{2}=\frac{b}{500}$

$b=250\sqrt{3}= 433\ m$

step 3

Find the distance AC+CB

$433+250=683\ m$

Subtract the distance AB from 683 m

$683-500=183\ m$

Answer 2

Answer:

a)183

Step-by-step explanation:

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