Two vertical poles of lengths 11 ft and 14 ft stand 16 ft apart. a cable reaches from the top of one pole to some point on the ground between the poles and then to the top of the other pole. where should this point be located to use 30 ft of cable?

We are given

total length of cable is 30 feet

and this cable is on hypotenuse sides of the triangles

so, we can draw triangle as

Let's assume those hypotenuse as 'a' and 'b'

so, we will have

now, we can find 'a' and 'b' from triangle

Smaller triangle:

Larger triangle:

we know that

so, we can plug this value

and we get

now, we can solve for x

now, we can use quadratic formula

we get

so,

The point should be located 4.510 feet , 9.627 feet from the smaller pole to use 30 feet cable............Answer

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12

look at the picture i have filled out a table for it. hope this .

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