Question

find the distance of gap d

Answer 1

Answer:

$\displaystyle d \approx 15.8768$

Step-by-step explanation:

We want to find the distance of d or AB.

From the right triangle with a 35° angle, we know that:

$\displaystyle \tan 35^\circ = \frac{50}{PB}$

And from the right triangle with a 42° angle, we know that:

$\displaystyle \tan 42^\circ = \frac{50}{PA}$

AB is PA subtracted from PB. Thus:

$\displaystyle d = AB = PB - PA$

From the first two equations, solve for PB and PA:

$\displaystyle \frac{1}{\tan 35^\circ } = \frac{PB}{50} \Rightarrow PB = \frac{50}{\tan 35^\circ}$

And:

$\displaystyle \frac{1}{\tan 42^\circ } = \frac{PA}{50} \Rightarrow PA = \frac{50}{\tan 42^\circ}$

Therefore:

$\displaystyle d = AB = \frac{50}{\tan 35^\circ} - \frac{50}{\tan 42^\circ}$

Using a calculator:

$\displaystyle d= AB \approx 15.8768$