Question

what is the length of AB

Answer 1

Answer:

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

Step-by-step explanation:

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

$\tan \theta=\dfrac{p}{b}=\dfrac{AB}{64}$  --------1

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

$\cot (90-\theta)=\dfrac{b}{p}=\dfrac{4}{AB}$

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

$\tan \theta=\dfrac{b}{p}=\dfrac{4}{AB}$  ---------2

From equation 1 and 2,

$\Rightarrow \dfrac{AB}{64}=\dfrac{4}{AB}$

$\Rightarrow AB^2=64\times 4$

$\Rightarrow AB^2=256$

$\Rightarrow AB=\sqrt{256}$

$\Rightarrow AB=16$