Question

What is the length of AB

Answer 1

ab = 16cm

Explanation:

Answer 2

`\boxed{\boxed{\overline{AB}=16}}`

Explanation:

In the triangle ABC, m∠ABC=90°. Hence, it is right angle triangle.

`\tan \theta=(p)/(b)=(AB)/(64)` --------1

In the triangle ABD, m∠ABD=90°. Hence, it is right angle triangle.

`\cot (90-\theta)=(b)/(p)=(4)/(AB)`

As
`\cot (90-\theta)=\tan \theta`, so

`\tan \theta=(b)/(p)=(4)/(AB)` ---------2

From equation 1 and 2,

`\Rightarrow (AB)/(64)=(4)/(AB)`

`\Rightarrow AB^2=64* 4`

`\Rightarrow AB^2=256`

`\Rightarrow AB=√(256)`

`\Rightarrow AB=16`