Respuesta :

calculista

Answer:

The answer is the option D [tex]AC=126\ units[/tex]

Step-by-step explanation:

we know that

The triangles EDC and ABC are similar

then

The ratio of their corresponding sides is equal

so

[tex]\frac{EC}{CA}=\frac{DE}{AB}[/tex]

substitute

[tex]\frac{x}{140-x}=\frac{9}{81}[/tex]

solve for x

[tex]9x=140-x\\9x+x=140\\x=140/10\\x=14\ units[/tex]

Find the length of AC

[tex]AC=140-x=140-14=126\ units[/tex]

Answer: Option D, the length of AC is 126 m


Step-by-step explanation:

In the triangle DEC, tan of angle DCE = DE/EC = 9/x


Now, In triangle BAC, tan of angle BCA = BA/AC = 81/(140-x)


Now, both angles DCE and BCA are equal.


Therefore, tan of angle DCE = tan of angle BCA


or, 9/x = 81/(140-x)

or, 140 - x = 9x

or, 140 = 10x

or, x = 14


So, length of AC = 140 - x = 140 - 14 =126


Hope it helps.


Thanks you :)


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