A strong wind breaks the trunk of a 42-meter-tall tree. The upper part of the tree tips over until its top hits the
ground. This upper part makes an angle of 55° with the ground. To the nearest tenth, how far up the trunk did
the tree break?

hey

let s note a and b the two numbers

we can write

(1) a = 2b - 2

(2) ab = 40

from (2) we can say for b different from 0 that

a = 40/b

replace it in (1)

40/b=2b-2

so

2(b-1)b = 40

b(b-1) = 20

5 is a trivial solution and as the product of the two solutions is -20 then the second solution is -4 therefore

<=> (b-5)(b+4) = 0

<=> b = 5 or b = -4

so we have

a= 40/b = 8 and b = 5

or

a = 40/b = -10 and b = -4

(8,5) and (-10.-4) are solutions

do not hesitate if you have any question

thanks