Two persons A and B are on the same side of a tower (T). If the angles of elevation of the top of the tower as observed by A and B are 40° and 55° respectively and line / AB / is 6m. Find the height of the tower.

12.21 m to the nearest hundredth.

Step-by-step explanation:

Let x m be the height of the tower.

Let y m be the distance from the closest person (B) from the tower.

Then we have the system:

tan 55 = x/y

tan 40 = x / (y + 6) (as line AB = 6)

From the first equation:

x = y tan 55

Substituting in the second equation:

tan 40 = (y tan 55) / (y + 6)

tan 40 (y + 6) = y tan 55

y tan 40 + 6 tan 40 = y tan 55

y (tan 40 - tan 55) = - 6 tan 40

y = - 6 tan 40 / (tan 40 - tan 55)

y = 8,547 m

From the first equation

tan 55 = x / 8.547

x = 8.547 tan 55

= 21.21. m