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.
Answer ↷
183 meters
Solution ↷
we know that,
In a right angled triangle
[tex]⇒cos \: 60° \: = \frac{adjacent \: side}{hypotenuse} \\ [/tex]
[tex]⇒cos \: 60° \: = \frac{BC}{AB} \\ [/tex]
[tex]⇒ \frac{1}{2} \: = \frac{a}{500} \\ [/tex]
[tex] ⇒a = 250 [/tex]
Also, we know that,
[tex]⇒sin \: 60° \: = \frac{opposite \: side}{hypotenuse} \\ [/tex]
[tex]⇒ \frac{ \sqrt{3} }{2} \: = \frac{AC}{AB} \\ [/tex]
[tex]⇒ \frac{ \sqrt{3} }{2} \: = \frac{b \:}{500} \\ [/tex]
[tex]⇒b = 250 \sqrt{3} = 433(approx)[/tex]
Now,
Distance covered to walk directly from building A to buliding B ↷
[tex]⇒AC+BC-AB[/tex]
[tex]⇒433 + 250 - 500[/tex]
[tex]⇒683 - 500[/tex]
[tex]⇒183m[/tex]
Hence , 183m distance will be require to walk directly from building A to buliding B
