Solve for x B 31° С 26 X= (Round to the nearest hundredth.)

Mathematics

1 answer:

ira [324]3 years ago

4 0

Answer:

S i neorrddints poy

Step-by-step explanation:asdadasdasdasdo

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A flagpole is secured on opposite sides by two guy wires, each of which is 5 ft longer than the pole. the distance between the p

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The height of the flagpole to the nearest inch is 388 inches.

Explanation

According to the below diagram, AB is the flagpole which is secured on opposite sides by two guy wires, AB and AC.

Suppose, the length of the flagpole(AB) is $x$ ft.

As each of the guy wires is 5 ft longer than the pole, that means $AC= AD= (x+5)ft$

Also given that, the distance between the points where the wires are fixed to the ground is equal to the length of one guy wire. That means, $CD= (x+5)ft$

As $\triangle ABC$ and $\triangle ABD$ are congruent to each other, so $BC=BD= \frac{1}{2}CD= \frac{1}{2}(x+5) ft$

Now in right triangle $ABD$ , using Pythagorean theorem......

$AB^2+BD^2= AD^2\\ \\ x^2+[\frac{1}{2}(x+5)]^2= (x+5)^2\\ \\ x^2+ \frac{1}{4}(x+5)^2 = (x+5)^2\\ \\ 4x^2+(x+5)^2= 4(x+5)^2\\ \\ 4x^2= 3(x+5)^2\\ \\ 4x^2=3(x^2+10x+25)\\ \\ 4x^2-3x^2-30x-75=0\\ \\ x^2-30x-75=0$