Question 729239
Let AP = 20 m
Let BQ = 30 m

AQ is one rope
BP is the other rope

They intersect at M

WE have to find MT

In triangle APQ 

Tan AQP = 20/50 = 2/5

Tan BPQ = 3/5

Let PT be y
QT = 50-y

Let MT =x

Tan MQT = x/(50-y) = 2/5

5x=2(50-y)
5x+2y=100.......................(1)

Tan MPT= x/y= 3/5

5x-3y=0.......................(2)


solve equations (1) & (2)

5.00	x	+	2.00	y	=	100.00	.............1		
Total value									
5.00	x		-3.00	y	=	0.00	.............2		
Eliminate	y								
multiply (1)by		3.00							
Multiply (2) by		2.00							
15.00	x		6.00	y	=	300.00			
10.00	x		-6.00	y	=	0.00			
Add the two equations									
25.00	x				=	300.00			
/	25.00								
x	=	12m							


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