Iwant diagram a vertical tower subtends a right angle on the top of 10m high flagstaff.if distance between them is 20m,find the height of the tower

Let us consider a triangle where AB to be the flagstaff of 10 m and BC to be of 20 m as the distance between the tower and the flag.  
Considering ABC and ADE as triangle
 AB = 10 = CE
 BC = 20 = AE 
 Calculating the values of ABC
 tan x = AB/BC
 tan x = 10/20
 10/tan x = 20(1) 
 Calculating the values of ADE
 tan(90-x) = DE/AE
 cot x = DE/20
 DE/cot x = 20 (2) 
 Solving equations 1 & 2
 10/tan x = DE/cot x
 DE = 40
 Hence the total height of the tower is DE+CE = 40+10= 50 m.

The first day the author reaches 100 days is on day 16.

To solve this problem, you could use a graphing calculator to graph the given equation. Then, determine when this line crosses 100. It crosses when x = 15.539. Therefore, we would have to round up to 16 so it is at least 100.

You could use the quadratic equation to solve: 100 = x^2 -12x + 45

Either you will get 16. If you use the quadratic formula, make sure to only use the positive answer.