Question

What is the length of AC

Answer 1

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

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 :)

Answer 2

The answer is the option D
`AC=126\ units`

Explanation:

we know that

The triangles EDC and ABC are similar

then

The ratio of their corresponding sides is equal

so

`(EC)/(CA)=(DE)/(AB)`

substitute

`(x)/(140-x)=(9)/(81)`

solve for x

`9x=140-x\\9x+x=140\\x=140/10\\x=14\ units`

Find the length of AC

`AC=140-x=140-14=126\ units`