Finding a Lenght Two vertical poles, one 8 ft tall and the other 24 ft tall, have ropes stretched from the top of each to the base of the other (see the figure). How high above the ground is the point where the ropes cross? [Hint: Use similarity]

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SabadisO · Accepted Answer

Given: One pole is 8 ft tall and other pole is 24 ft tall. Both have ropes stretched from the top of each to the base of the other.  Figure(1) Approach: If all three angles of a triangle are equal to corresponding angles of the other triangle, then both the triangles are similar and the rule is referred to as AAA rule. Calculation: By AAA rule, triangle AEF is similar to triangle ADC. So, AEh=AE+EDDC =AE+ED24...(1) By AAA Rule, triangle BAD is similar to triangle FED. So, EDh=AE+EDAB =AE+ED8 AE+ED=8EDh...(2) Substitute value AE+ED from equation (2) in equation (1). AEh=8EDh/24=8ED24h AE=ED3 Substitute ED3 for AE in Equation (2). AE3+ED=8EDh 4ED3=8EDh 43=8h h=3×84 =6 Therefore, the height of the point above the ground where the ropes cross is 6 ft.

Finding a Lenght Two vertical poles, one 8 ft tall and the other 24 ft tall, have ropes stretched from the top of each to the base of the other (see the figure). How high above the ground is the point where the ropes cross? [Hint: Use similarity]

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