CPhill

Look at line 3....(Grosss amount due from borrower)..it says  to add (1) and (2)...what is this amount ??

Look at the amount next to the  "County taxes (half year)......what is that amount ??

We can find the area of this triangle using Heron's Formula

s  =  [ 22 + 12 + 14 ] / 2  = 48/2  =  24

The area is given by :

√[ 24 (24 - 22) (24 - 12) (24 - 14)  = √ [24 * 2 * 12 * 10 ]  = √[48 * 120] = 24√10

Because the radius of the inscribed circle is perpendicular to each side of the triangle...three triangles are formed.......each with a height = to the circle's radius and with bases of 22, 12 and 14 respectively

So...the area of the triangle can be expressed as

Area  = (1/2)r [ 22 + 12 + 14]     where r is the altitude of each triangle = the radius of the inscribed circle

Solving for r we have

r  =   2* Area / [ 22 + 12 + 14 ]   =

2 * 24√10 / [ 48]  = 

48√10 / 48 =

√10  units

We can omit any one of the digits  and have the possible sums

Omit       Sum

   1           27

   2           26

   3           25

   4           24

   5           23

   6           22

   7           21

So.....the probability  of a sum of 24  is   1 / 7

These angles will sum to  180°

So

x  + 4x  = 180

5x  = 180

x  = 36°  ⇒  measure  of the smaller interior angle

x^2 + 20  =

(x + i√20 ) (x - i√20)  =

(x + 2i√5 ) ( x - 2i√5 )

Ah...i made a slight mistake....

(1/2)sin (4x)  =

(1/2)  sin (2 * 2x)  =

(1/2) (2 sin 2x  cos 2x)  =

(sin 2x) (cos 2x)  =

(2sinx cos x) * ( 1 - 2 sin^2 x)  =

2sin xcosx  - 4sin^3x cos x   =  the right hand side

Now corrected

Yep...small mistake...let me correct that  !!!